Simplicial quantum gravity provides a framework that preserves the full 4-dimensional nature of spacetime, making it specially suited to deal with topological issues. Additionally, simplicial quantum gravity leads to simplicial minisuperspace approximation in a more natural way than its continuum counterpart. The simplicial minisuperspace models have the advantage of still preserving the full 4-dimensional treatment of spacetime, not depending on any arbitrary (3+1) decomposition. There is also the possibility of systematic improvement. In this dissertation we investigate how the simplicial framework might provide vital clues about what histories to consider in the sum yielding the wavefunction of the universe. In order to obtain concrete results we examine these issues in the simplicial minisuperspace approximation. The results obtained are in support of extending the space of histories to include conifolds and not just manifolds. We use simplicial minisuperspace models to investigate the quantum cosmology of a vast range of universes, obtaining the wavefunction of the universe for all universes whose spatial boundary is a combinatorial 3-manifold with a common edge length, in the presence of a massive scalar field. We then extend those results to a specific combinatorial 3-manifold with two different edge lengths. We also consider a model with arbitrary scalar coupling of the scalar field to gravity. In all these cases we find that the resulting wavefunctions predict classical Lorentzian spacetime for the late universe. We then investigate a simplicial wormhole configuration. Since we deal with spacetime in a 4-dimensional way, the same model can breach the usual gap between the study of Euclidean and Lorentzian wormholes. We obtain a prediction for a natural Planck scale for Euclidean wormholes, which is supported by similar results for Lorentzian continuum minisuperspaces.