Stream depletion due to groundwater extraction by wells may cause impact on aquatic ecosystem in streams, conflict over water rights, and contamination of water from irrigation wells near polluted streams. A variety of studies have been devoted to addressing the issue of stream depletion, but a fundamental framework for analytical modeling developed from aquifer viewpoint has not yet been found. This review shows key differences in existing models regarding the stream depletion problem and provides some guidelines for choosing a proper analytical model in solving the problem of concern. We introduce commonly used models composed of flow equations, boundary conditions, well representations and stream treatments for confined, unconfined, and leaky aquifers. They are briefly evaluated and classified according to six categories of aquifer type, flow dimension, aquifer domain, stream representation, stream channel geometry, and well type. Finally, we recommend promising analytical approaches that can solve stream depletion problem in reality with aquifer heterogeneity and irregular geometry of stream channel. Several unsolved stream depletion problems are also recommended.