The rapid globalization of the energy crisis and the adverse effects of global warming have caused the need for non-conventional energy resources to be felt more than ever. As a result of this, vertical axis wind turbines (VAWT) have received much attention over the recent decades, and have thus been more developed and used worldwide. The cross-flow wind turbine (CFWT) is a wind turbine in the category of VAWTs, and perfectly suitable for urban applications due to its simplicity, high starting torque at low wind speed, and self-starting capability, even though its low power coefficient as its main drawback has slowed down its widespread use so far. The main aim of this paper is to review the scientific literature and recent developments in the field of CFWTs. The governing equations and turbulence models for the simulation of the turbine are discussed and various wind resource assessment methods for estimating potential site locations, different aspects, and wind energy harvesting systems from buildings are debated. The research gaps, challenges, and future possible works on such turbines and their applications are discussed. Investigations indicate that changing the rotor geometric parameters and adding innovative augmentation devices have been the most widely addressed approaches for making performance enhancement of the wind turbine in the literature. The critical performance-affecting parameters are improved by various innovative designs of the turbine structure or blades, as well as several augmentation techniques, such as guide nozzle, casing, windshield, guide vane, deflector, cowling, etc.