Lorentz force-based flow control in materials with low electrical conductivity has a long history back to the first half of the 19th century. This review will focus on developments during the last two decades, collecting results from numerical simulations and laboratory experiments. Typically, the actuators consist of permanent magnets and electrodes flush-mounted with the surface, generating Lorentz forces in the fluid layers adjacent to the wall. We will discuss the application of Lorentz forces to reduce friction drag in turbulent boundary layers and to delay boundary layer transition. The control of separated flows and shear layers is another key aspect of the review. Energetic efficiency, one of the main criteria for flow control, and its relation to typical operating conditions will be analyzed as well. Lorentz forces can be successfully used to control a broad range of flow phenomena and are a versatile tool for basic fluid dynamics research. However their current applicability in large scale systems is hampered by the low electrical to mechanical efficiency intrinsic to actuators based on the magnetic fields delivered by today's permanent magnets. © 2013 EDP Sciences and Springer.