Abstract: Over the last ten years, experimental advances with ultracold quantum gases in optical lattices have made possible the study of various interesting many-body phenomena that are difficult to observe in solid-state systems. Not only do these systems allow the investigation of interesting quantum phases, but they offer unique opportunities for the study of non-equilibrium dynamics, addressing fundamental questions such as the mechanisms behind thermalization in closed quantum systems or the behavior of a system after a quantum quench. I will discuss our recent work in coherent and dissipative many-body dynamics, focused around these ideas as well as the key challenge in experiments of producing many-body states with low temperature and entropy. In this context it is important to characterize and control the competing heating mechanisms in the experiment, which can arise from various sources, including incoherent scattering of the lattice light (spontaneous emissions), and typically have effects that depend strongly on the detailed characteristics of the many-body state. Spontaneous emissions tend to localize atoms on particular lattice sites, in that sense acting as a type of local quantum quench. Computing dynamics described by a many-body master equation, we investigate such quenches for bosons moving in 1D in the lattice system. We identify both regimes in which simple observables relax rapidly to a thermal distribution at higher temperature, and other regimes where the system settles on a short timescale to a non-thermal state. I will also discuss adiabatic state preparation techniques, and how they could be useful in preparing many-body states in a variety of systems, including crystalline states of Rydberg atoms.