Ions in solution play a central role in most electrochemical systems. Theoretical approaches rooted in continuum models, such as Debye-Hückel theory or the Born solvation model, provide the basis for much of our understanding about processes that involve dissolved ions. Despite the remarkable success of these relatively simple theories, their (drastic) assumptions can sometimes lead to a qualitatively incorrect description of the underlying chemical physics. Here, we will overview recent work from molecular simulations that casts light on the molecular details of both equilibrium and nonequilibrium processes in solution. Implications for relating the details of microscopic relaxation processes to experimental observables such as impedance and capacitance will also be discussed.