Using direct numerical simulations, we provide a thorough study regarding the electrokinetics of ionic liquids. In particular, modified Poisson-Nernst-Planck equations are solved to capture the crowding and overscreening effects characteristic of an ionic liquid. For modeling electrokinetic flows in an ionic liquid, the modified Poisson-Nernst-Planck equations are coupled with Navier-Stokes equations to study the coupling of ion transport, hydrodynamics, and electrostatic forces. Specifically, we consider the ion transport between two parallel charged surfaces, charging dynamics in a nanopore, capacitance of electric double-layer capacitors, electroosmotic flow in a nanochannel, electroconvective instability on a plane ion-selective surface, and electroconvective flow on a curved ionselective surface. We also discuss how crowding and overscreening and their interplay affect the electrokinetic behaviors of ionic liquids in these application problems.