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