Well-known problems with standard big-bang cosmology motivate the inflationary scenario. A large class of inflationary models can be described using the slow-roll formalism, in which a set of interacting classical scalar fields drives the expansion of the very early universe. In order to explain how inflation ends while quickly reheating the universe, many slow-roll models are constructed to contain a parametric-resonance-driven preheating phase. This phase is driven by non-perturbative processes, and fully understanding its properties requires the use of 3-D numerical simulations. I will discuss PSpectRe, a pseudo-spectral code for simulating post-inflationary preheating. Compared to existing codes, PSpectRe displays excellent convergence, and can often obtain reliable results using a substantially smaller number of grid points. A generic class of preheating models has been predicted to generate a copious quantity of oscillons. Oscillons are long-lived, oscillatory, spatially localized solutions to nonlinear scalar-field models. Using PSpectRe, oscillon-generating preheating models have been investigated, and it has been confirmed that a large class of these models predicts a post-preheating oscillon-dominated phase. In such an oscillon-dominated phase, the universe evolves as would a traditional matter-dominated universe, and this significantly alters how these models must be evaluated. Initial applications of PSpectRe to investigating gravitational-wave observables also will be discussed.
