A basic overview
Resources:
From McBride:
Gradually the apostles and their successors developed the Eucharistic celebration into the structure that endures to this day. They first named it the “Breaking of the Bread” but soon they saw the need to separate the rite from a meal, both because of abuses at meals (1 Cor 11:17-22) and because they wanted a more prayerful setting for this act of worship.
This development was reported by a late first-century document, the Didache or “Teaching of the Apostles.” Eucharist was moved to Sunday in memory of Christ’s resurrection. In place of the meal the early Christians created a Liturgy of the Word somewhat modeled after synagogue prayer that included readings from Scripture, singing of psalms and an instruction.
Around the words of institution they added prayers of thanksgiving, praise and intercession. By the year 150, St. Justin Martyr tells us that the basic structure of the Mass was already in place. These Eucharists were held in people’s homes up until the year 313.
On Sunday there were two readings by a lector, a homily by the priest, then the Eucharistic Prayer and the distribution of Communion. And yes, there was a collection—for widows, orphans and others in need! The threefold roles of bishop, priest and deacon were already in place in the first century.
Our Second Eucharistic Prayer today is brief and simple, and owes its inspiration to a similar one composed by Hippolytus of Rome in 215. It is clear that the basic form of the Eucharist occurred very early and has remained remarkably durable for 2,000 years.
Communion is reserved to Christians as a matter of logical utility. What would it do for me to receive the Eucharist without belief? As a basic reenactment of the Last Supper, it is an act of faith that invites and receives a blessing. Without faith, one cannot do this; how can one ask for and receive what they do not believe is real?
Still, though, according to
Wikipedia:
Many Christian denominations classify the Eucharist as a sacrament. Some Protestants prefer to call it an ordinance, viewing it not as a specific channel of divine grace but as an expression of faith and of obedience to Christ ....
.... Christian denominations differ in their understanding of whether they may receive the Eucharist with those with whom they are not in full communion. The famed apologist St. Justin Martyr (c. 150) wrote: "No one else is permitted to partake of it, except one who believes our teaching to be true...." For the first several hundred years, non-members were forbidden even to be present at the sacramental ritual; visitors and catechumens (those still undergoing instruction) were dismissed halfway through the Liturgy, after the Bible readings and sermon but before the Eucharistic rite. The Divine Liturgy of St. John Chrysostom, used in the Byzantine Churches, still has a formula of dismissal of catechumens (not usually followed by any action) at this point.
The ancient Churches, such as the Roman Catholic and the Eastern Orthodox exclude non-members from Communion under normal circumstances, though they may allow exceptions, e.g., for non-members in danger of death who share their faith in the reality of the Eucharist and who are unable to have access to a minister of their own community. Some Protestant communities including Lutheran churches in the ELCA, LCMS, and WELS practice closed communion and require catechetical instruction for all people before receiving the Eucharist. Most Protestant communities, including Reformed, Evangelical, Methodist, the Church of Sweden, and some ELCA Lutherans and Anglicans practice open communion in the sense of not limiting it to members of their own Church alone, but some of them require that the communicant be a baptized person.
Some Progressive Christian congregations offer communion to any individual who wishes to commemorate the life and teachings of Christ, regardless of religious affiliation.
Not all denominations practice communion, but the vast majority do.