Can I hear about the alternative models to the Big Bang and why they've been rejected?

Hey sure. After the big bang was proposed first in the 1930s, its main competitor was the steady state model, which proposed that the universe was expanding infinitely, but that new matter was constantly being created to fill in the gaps. But astronomical observations of galaxies and the discovery of the Cosmic Background radiation in the 1960s definitively proved that there was an initial "fireball" as described by the Big Bang. So the Steady State model was dropped. After this, an oscillating model in which the universe went through infinite cycles of big bang and big crunch was proposed. But this too has been abandoned, discredited by the 2nd law of thermodynamics, and the observation that the universe seems now to be accelerating in expansion; it's not slowing down to eventually re-collapse.

At the moment, two more models, eternal inflation and brane cosmology (which is a form of string theory) are being explored. Eternal inflation itself is a modification of the big bang theory, and claims the universe could be expanding infinitely in regions we don't see. String theory and its variants like brane cosmology and M-theory envision all matter and physics being explained by 10 or 11-dimensional strings or "branes" that are far smaller than we could ever detect. But both these theories and the various models under them are actually subject to the Borde-Guth-Vilenkin theorem or have been otherwise shown to require a beginning anyway. As Alexander Vilenkin himself has said, summarizing the current state of the science: "There are no models at this time that give us a satisfactory model for a universe without a beginning." (Alexander Vilenkin, 2012)

So, despite all the attempts to theorize away the beginning of the universe, the current evidence and theory points us to a universe that began, and therefore a universe that requires a cause or an explanation.

For further information see Contemporary Cosmology and the Beginning of the Universe on Reasonable Faith Q&A.