We present an analysis of hydrodynamic effects in systems involving ion transport from an aqueous electrolyte to an ion-selective surface. These systems are described by the Poisson-Nernst-Planck and Navier-Stokes equations. Historically, such systems were modeled by one-dimensional geometries with spatial coordinate in the direction of transport and normal to the ion-selective surface. Rubinstein and Zaltzman [JFM 579, 173-226 (2007)] showed that when such systems are unbounded in the transverse directions, a hydrodynamic instability can occur. This instability, referred to as electroconvective instability, leads to advective mixing, which results in overlimiting transport rates significantly beyond what is predicted from one-dimensional models. In this study, we present an analysis of electroconvection in confined systems, considering a broad range of applications including microfluidic systems and porous media. Our analysis reveals that full confinement in the transverse directions significantly suppresses electroconvection and overlimiting current. However, when at least one transverse direction allows for flow escape, such as in thin but wide channels or in porous media, the onset of instability is only weakly affected by confinement. We will also present a review of relevant literature and discuss how the present study resolves the contradictory contrasts between the results of recent work on this topic.