The principle of electrohydrodynamics (EHD) processes relies on manipulating fluids using electric forces. The advantage of EHD over other fluid manipulation approaches, such as thermal or acoustic-based processes, consists in its excellent controllability, versatility (in terms of the range of suitable fluids), and relatively low cost. The importance of modeling and simulation of EHD processes, particularly for the microsystems, has been growing over the past decade, replacing on many occasions trial-and-error approaches. The present paper is devoted to the advances in the numerical modeling and simulation of electrohydrodynamic (EHD) problems. Physical phenomena playing an essential role in EHD are explained and governing equations are formulated. Major challenges faced when modeling EHD problems are highlighted and different classes of numerical approaches used for handling them are outlined. Benefits and disadvantages as well as open issues in different numerical approaches are also discussed. Finally, the paper provides an overview of numerical studies of EHD in multi-phase micro-systems emphasizing some key findings for three classes of problems, namely droplets, jets and planar films exposed to external electric fields.