String gas cosmology is a natural approach to cosmology within string theory. Two of its novelties are that it provides means to replace the singular evolution of the early universe with a smooth, possibly cyclic phase and that it suggests a dynamical mechanism for selecting at most three spatial dimensions that can grow large cosmologically. This work presents some progress in these two directions. By implementing simple corrections to gravitational dynamics, it is shown how string gas cosmology can give rise to cyclic and bouncing models in the early universe. These models have some attractive features such as an eventual exit to a radiation dominated, big-bang-like expanding universe, and a loitering phase that can address the horizon problem of standard big-bang cosmology. Regarding decompactification, the Brandenberger-Vafa mechanism is explored, and it is shown that within the framework of string gas cosmology, a semiclassical treatment of fundamental string interactions in the early universe largely favors the growth of three, and not more, spatial dimensions to cosmological scales.