Short answers, pulled from the story.
Paschasius Radbertus claimed that the bread and wine used in the Eucharist actually became the body and blood of Jesus in their very substance. He argued this was a physical reality where the substance of the bread was wholly changed into the substance of Christ's body, even though the taste, color, and texture remained exactly the same.
The earliest written account of the Last Supper comes from the First Epistle to the Corinthians, written by the Apostle Paul in the early 50s of the 1st century. This text predates the Gospels themselves and records Jesus saying, This is my body, which is for you. Do this in remembrance of me.
The belief in the real presence of Christ in the Eucharist led to accusations that Jewish people were stabbing or physically harming communion wafers in a ritual known as host desecration. These accusations were used to promote anti-Jewish ideology and violence, drawing parallels between the destruction of the host and the killing of Christ himself.
The Marburg Colloquy of 1529 resulted in a failure to agree on the nature of the Eucharist, with Martin Luther insisting on the real presence and Huldrych Zwingli arguing that the bread and wine were merely symbols. This disagreement prevented the formation of a unified Protestant front and led to denominations developing their own distinct practices.
The Eastern Orthodox churches do not attempt to define exactly how the change occurs, preferring to leave it as a holy mystery rather than a philosophical proposition. They reject the Aristotelian terminology of substance and accidents used by the Catholics and instead speak of transelementation or simply the change, focusing on the result rather than the process.