Within the inflationary paradigm, our patch of the universe near the end of inflation is highly homogeneous and isotropic as necessitated by cosmic microwave background observations. This patch, however, is also in a cold and non-thermal state. A successful model of an inflationary primordial universe should account for how the universe transitioned from an inflationary to a radiation-dominated, hot, thermal phase required for the production of light elements via big-bang nucleosynthesis. It is desirable for such a model also to include a mechanism for the generation of the observed matter-antimatter asymmetry and perhaps a primordial mechanism for the generation of cosmic magnetic fields.

The transition from an inflationary to a radiation-dominated, thermal phase (reheating) is likely to be phenomenologically rich. Reheating could include explosive particle production and various other non-perturbative, non-linear and non-equilibrium phenomena. Reheating can leave its own observational signatures in the form of gravitational waves and non-Gaussianities. Importantly, reheating can also affect the observational predictions of the preceding phase of inflation. Reheating remains an active field of research, with significant gaps in our understanding of the process. This thesis is an attempt to improve our understanding of the period following inflation, including reheating, through an exploration and analysis of realistic post-inflationary models with the aid of detailed numerical simulations. The focus of the studies is on aspects of the models with potential observational implications.

In Part I of this thesis, we provide an overview of inflation and its end, concentrating on our current understanding of reheating and the challenges we face in trying to constrain reheating observationally.

In Part II, we consider the post-inflationary expansion history in a broad class of observationally-favoured single-field models of inflation. Generally, the ambiguity in the expansion history of reheating can cause significant uncertainty in predictions for inflationary observables such as the spectral index, $ns$, and the tensor-to-scalar ratio, $r$. The work in this part considers the full non-linear evolution of the inflaton during the initial stages of reheating and places bounds on the post-inflationary expansion history when perturbative couplings of the inflaton to other relativistic fields are included.

In Part III, we investigate non-perturbative particle production and non-linear dynamics after inflation in models where the inflaton is charged under global/local symmetries. We first explore the effects of the non-linear inflaton dynamics for the generation of matter-antimatter asymmetry in the case where a global $U(1)$ symmetry of the inflaton is weakly broken. We find a parameter range in which the model successfully predicts the observed baryon-to-photon ratio. We then consider the particle production during and after inflation in models with a charged inflaton under Abelian, $U(1)$, and non-Abelian, $SU(2)$ and $U(1)\times SU(2)$, gauge symmetries. Finally, we present a novel algorithm for evolving the full set of coupled, non-linear equations describing the $U(1)$ charged inflaton and accompanying gauge fields on a lattice in an expanding universe. The novel feature here is that the gauge constraints are satisfied to machine precision when the gravitational dynamics are self-consistently included at the background level, and there are no restrictions on the order of the time-integrators.