In this review, the application of a wide variety of external electric fields in molecular simulation shall be discussed, including time-varying and electromagnetic, as well as the utility and potential impact and prospects for exploitation of such simulations for real-world and industrial end use. In particular, non-equilibrium molecular dynamics will be discussed, as well as challenges in addressing adequate thermostatting and scaling field amplitudes to more experimentally relevant levels. Attention shall be devoted to recent progress and advances in external fields in ab initio molecular simulation and dynamics, as well as elusive challenges thereof (and, to some extent, for molecular dynamics from empirical potentials), such as timescales required to observe low-frequency and intensity field effects. The challenge of deterministic molecular dynamics in external fields in sampling phase space shall be discussed, along with prospects for application of fields in enhanced-sampling simulations. Finally, the application of external electric fields to a wide variety of aqueous, nanoscale and biological systems will be discussed, often motivated by the possibility of exploitation in real-world applications, which serve to underpin our molecular-level understanding of field effects in terms of microscopic mechanisms, and possibly with a view to control thereof.