I have recently been in a rather hearty debate with a close brother in the Lord on this matter of the nature of the Lord’s Supper. Such has caused me to spend some more time looking into the various views, particularly those centered in Reformed Theology. Well, the following is simply an overview of four views on the Lord’s Supper (Roman Catholic, Lutheran, Zwingli, and Calvin). This is directly taken from R. C. Sproul’s book, Essential Truths of the Christian Faith. Of course, we, as Evangelical/Reformed Christians, do not hold to the Roman Catholic view. I will say now that I am personally torn between Zwingli’s “memorial” view and Calvin’s “real presence” view. Now, Zwingli of course believed in Christ’s presence during the Lord’s Supper, just not in the same sense as Calvin, who believed in the real presence of the body and blood of Christ, but in a spiritual sense, not in a physical sense.
In short, I see Zwingli’s view as attempting to not go too far beyond the clear and simple words of Christ in the institution of the Lord’s Supper. On the other hand, while I don’t necessarily disagree with Calvin, some of what he posits seems, at least to me, to fall into a bit of “over theologizing,” to the point where one has a hard time seeing the elaborate theology in the simple and clear statements of Christ. For instance, Sproul references the continual presence of Christ with His Church as Calvin’s support for His view (Matt. 28:20). However, is not the means of Christ’s abiding presence the Holy Spirit (Jn. 14-16; Acts 1:1-8)? Further, this presence of Christ is not something that comes and goes (i.e. during the observance of the Supper), but is ever-present. No doubt, there is a sense in which God manifests His presence more fully in the corporate gathering of His people (Matt. 18:20; Acts 4:31). I’m also a bit confused at the idea of the physical body and blood being spiritually present, as being based on Christ’s divine nature. After all, the divine nature is not physical, but spirit (Jn. 4:24). It further appears that Calvin takes the view that Christ’s divine nature comes down to commune with us during the Supper, and at the same time we, in some mystical sense, go up to commune with His physical body (see last paragraph). Perhaps I’m just misunderstanding Calvin’s points. Anyways, these are just some of my thoughts. A further study of both views is needed. For now, I simply present to you this simple overview from Sproul [pp. 241-243]:
Martin Luther rejected the Roman Catholic doctrine of transubstantiation, that is, that the Communion bread and wine are changed into the actual body and blood of Christ. Luther saw no need for this doctrine. Rather, he agreed that Christ’s presence did not replace the presence of bread and wine but was added to the bread and wine. Luther maintained that the body and blood of Christ are somehow present in, under, and through the elements of bread and wine. It is customary to call the Lutheran view consubstantiation because the substance of the body and blood of Christ are present with (con) the substance of bread and wine. Lutheran theologians, however, do not like the term consubstantiation and protest that it is understood in terms that are too closely associate with the Roman Catholic doctrine of transubstantiation.
But it is clear that Luther insisted on the real physical and substantial presence of Christ in the Lord’s Supper. He repeatedly cited Jesus’ words of institution, ‘this is My body,’ to prove his point. Luther would not allow the verb is to be taken in a figurative or representative sense. Luther also adopted the doctrine of the communication of attributes by which the divine attribute of omnipresence was communicated to the human nature of Jesus, making it possible for His body and blood to be present at more than one place at the same time.
Ulrich Zwingli and others argued that Jesus’ words ‘this is My body’ meant really ‘This represents [i.e. signifies; points to] My body.’ Jesus frequently used the verb to be in such a figurative sense. He said, ‘I am the door,’ ‘I am the true vine,’ etc. Zwingli and others argued that Christ’s body is not present in actual substance at the Lord’s Supper. The supper is a memorial only, with Christ’s presence no different from His normal presence through the Holy Spirit.
John Calvin, on the other hand, when he debated with Rome and Luther, denied the ‘substantial’ presence of Christ at the Lord’s Supper. Yet when he debated with the Anabaptists, who reduced the Lord’s Supper to a mere memorial, he insisted on the ‘substantial’ presence of Christ.
On the surface it seems that Calvin was caught in a blatant contradiction. However, upon closer scrutiny we see that Calvin used the term substantial in two different ways. When he addressed Roman Catholics and Lutherans, he used the term substantial to mean ‘physical.’ He denied the physical presence of Christ in the Lord’s Supper. When he addressed the Anabaptists, he insisted on the term substantial in the sense of ‘real.’ Calvin thus argued that Christ was really or truly present in the Lord’s Supper, though not in a physical sense.
Because Calvin rejected the idea of the communication of attributes from the divine nature to the human nature, he was accused of separating and dividing the two natures of Christ and committing the Nestorian heresy, which was condemned at the Council of Chalcedon in A.D. 451. Calvin replied that he was not separating the two natures but distinguishing between them.
The human nature of Jesus is presently localized in heaven. It remains in perfect union with His divine nature. Though the human nature is contained in one place, the person of Christ is not so contained because His divine nature still has the power of omnipresence. Jesus said, ‘I am with you always, even to the end of the age’ (Matthew 28:20). [Sproul produces two diagrams/illustrations which I cannot here produce] Calvin taught that though Christ’s body and blood remain in heaven, they are spiritually ‘made present’ to us by Jesus’ omnipresent divine nature. Wherever the divine nature of Christ is present, He is truly present. This is consistent with Jesus’ own teaching that He was ‘going away’ yet would abide with us. When we meet Him at the Lord’s Supper we commune with Him. By meeting us in His divine presence, we are brought into His human presence mystically, because His divine nature is never separated from His human nature. The divine nature leads us to the ascended Christ, and in the Lord’s Supper we have a taste of heaven.
Summary:
1. Luther taught that the body and blood of Christ were added in, under, and through the elements of bread and wine.2. Zwingli taugh tht ememorial view of hte Lord’s Supper.
3. Calvin denied the physical presence of Christ at the Lord’s Supper, but affirmed the real presence of Christ.
4. Jesus’ human nature is localized in heaven; His divine nature is omnipresent.
Biblical Passages for Reflection: Matthew 26:26-29; 1 Corinthians 10:13-17; 11:23-34
Reformed Baptist Daily 
The following is John Calvin’s understanding of the sacraments (though I only include the Lord’s Supper for our purposes here). It is taken from his Truth for All Time, which basically served as a summary and outline for his Institutes. He wrote this before his Institutes, so he obviously elaborated on the sacraments in the Institutes, and perhaps even modified his view somewhat (?), but I can really grasp onto his words here (so long as I am understanding him correctly).
John Calvin (Truth for All Time)
1. The Necessity of the Sacraments
The sacraments have been instituted to exercise our faith before both God and men.
Before God, they exercise our faith by strengthening it in God’s truth. For the Lord knows that it is helpful to the ignorance of our flesh that he should present high and heavenly mysteries to us by means of perceptible realities. This is not to imply that such qualitites are inherent in the nature of the things offered to us in the sacraments. It is, rather, the Word of the Lord which stamps them with such a meaning. The promise, contained in the Word, always comes first; the sign is added to confirm and seal this promise, and, as it were, to make us more sure of it, for the Lord sees that this procedure suits our poor learning capacities. Our faith is so small and weak that unless it is propped up on all sides and upheld by all available means, it is suddenly and totally shaken, troubled and caused to totter.
Before men, the sacraments exercise our faith, for faith then expresses itself in a public confession and is thus prompted to praise the Lord.
2. What a sacrament is
A sacrament is an external sign by which the Lord depicts and bears witness to his good will towards us, in order to support the weakness of our faith.
To put it more briefly and clearly, a sacrament is an expression of the grace of God declared by an external sign.
The Christian church makes use of only two sacraments: Baptism and the Supper.
[Skip ahead to the Lord’s Supper]
4. The Lord’s Supper
The promise accompanying the mystery of the Supper openly declares why it was instituted and with what aim.
This mystery assures us that the Lord’s body was once given for us, in such a way that it is now ours and always will be. It assures us that his blood was once shed for us, in such a way that it will always be ours.
The emblems [elements] of this mystery are the bread and wine through which the Lord holds out to us the true communication of his body and blood. We are talking of spiritual communion, which is effected by the bond of the Holy Spirit alone, and which in no way requires a presence enclosed in Christ’s flesh through the bread or his blood through the wine. For although Christ, exalted in heaven, has left behind this earthly abode in which we are still pilgrims, yet no distance can dissolve his power by which he feeds his people with himself. Although they are very far from him, by this power he grants them to enjoy a communion with himself which is nonetheless very close.
So it is that in the Supper the Lord gives us teaching which is so certain and unmistakable that we must be assured without doubt that Christ, with all his riches, is there presented to us, no less than if he were placed before our eyes and touched by our hands.
The power and efficacy of Christ are such that, in the Supper, he not only brings to our spirits an assured confidence of eternal life, but he also makes us certain of the immortality of our flesh. For our flesh is already given life by his immortal flesh and, in some way, shares in his immortality.
This is why the body and blood are represented to us by means of bread and wine, so that we learn not only that they are ours, but that they are life and nourishment for us. Thus when we see the bread consecrated as the body of Christ, at that moment we should see this parallel in our minds: as bread feeds and preserves the life of our body, so the body of Christ is the nourishment and protection of our spiritual life. And when the wine is presented to us as an emblem of the blood, we must similarly consider we are receiving from Christ’s blood, in a spiritual way, the same benefits that wine brings to the body.
Thus this mystery, in the same way as it teaches us how great is God’s liberality towards us, also exhorts us not to be ungrateful towards such manifest generosity, but rather to exalt it with fitting praises and to extol it with thanksgiving.
Finally, this sacrament exhorts us to join with each other in the same sort of unity in which the members of a body, linked as they are, are bound together. For no stronger or sharper spur could be given to move and encourage us to mutual love than this: Christ, in giving himself for us, does not only invite us by his example to give and consecrate ourselves to each other, but makes himself to be shared by all, and also makes us all one in himself.