One of the best sources on this is Bart Ehrman. He's written a lot of popular works on it, as well as more academic articles and books as well. He has a great book called the Apocryphal Gospels that go over some of the texts that didn't make it into the New Testament. Elaine Pagels also has a more focused work on the Gnostic Gospels.

So there were other books and letters that simply didn't make the cut. And in fact, the book of Hebrews and Revelations almost didn't make the cut. The book of Hebrews was only added because it was thought to have been authored by Paul.

However, when looking at the creation of the Bible, we really aren't looking at Popes or other influential people pulling their weight. When we look at the Old Testament, by the time of Christianity, the canon was largely set. The main contention would later be whether or not the Greek texts should be included in the Old Testament. These texts, often referred to as the Deuterocanonical books or the Old Testament Apocraphya, were rejected by Jews as they were seen as more Hellenistic, but they were still contained within the Septuagint, the Greek translation of the Old Testament, which Christians inherited. Protestants would later reject the books as well, and they were never held to the same regard as rest of the Old Testament.

When it comes to the New Testament, we have a pretty well established canon around the 4th century and probably in the 3rd century. This canon is what became the New Testament we have today.

Here is where it gets a bit complicated. Ehrman has a great book called Lost Christianities (I'm really suggesting Ehrman as he writes in a way that the lay reader can really follow, and when he disagrees with the consensus among scholars, he points that out) where he details the various forms of Christianity. And these different groups of Christians ended up having different books. So we had the proto-orthodox/orthodox group, which became Catholicism, and then we had a wide array of different groups, probably most famous were the Gnostics.

These groups begin to appear more in the second century and blossomed. As they became more separated from what would become Catholicism, we end up seeing more and more books being produced. Even within the mainstream form of Christianity, later books would also be produced for a variety of reasons.

Something else happened in the second century. Marcion, who was within the proto-orthodox church to begin with and then later left forming a group we know as the Marcionites, created what is probably the first New Testament Canon. He focused on Paul, so he had a selection of the letters of Paul, and the Gospel he subscribed to was a form of Luke (some argue that he edited his copy of the Gospel of Luke, while others argue that it was either a modified Luke he inherited, or possibly even a proto-Luke or draft of Luke he had). Marcion, while pretty unknown today, had a pretty big impact on his time.

As Marcion was pushing out his canon, this seems to have pushed others to put together an official canon. The criteria that was looked at, which we garner from early church fathers, is that the books had to be early and attached to an authority figure. The four Gospels we have were already attached to early followers. Paul was included and we get a mix of his authentic letters, letters written in his name, and then Hebrews which was attached to him. Then we have letters from other early figures. The key though is that they had to be early. So we are talking about things that had already been around for some time in the second century.

We didn't get all of the early works. For instance, there are Pauline letters we know he wrote, as he mentions them, but we don't have them.

Later works simply were not considered. Works from other groups weren't considered. While they were technically Christian works, they weren't from the orthodox group, so they were ignored.

So we end up with a pretty clear canon quite early on, and it really didn't change in any significant ways by Popes or people of importance.