This article reviews Flux-Weakening (FW) algorithms for Permanent Magnet Synchronous Machines (PMSMs), focusing on the automotive sector, especially in electric and hybrid electric vehicles. In the past few years, the spread of Electric Vehicles (EVs) has improved the technology of electric machines and their control to achieve more compact and competitive solutions. PMSMs are the most widespread electric machines used in EVs thanks to their high-power density and potential operation at constant power range during high speed. Such high speed implies a high electromotive force. An FW technique is mandatory to reduce the electromagnetic flux generated by the electric machine due to the voltage limits of the traction inverter and the energy source. This article classifies and analyses the state-of-the-art FW control strategies by comparing their main advantages and drawbacks. The Vector Current Control (VCC) method that regulates the modulus of the applied voltage is the most common one in the literature thanks to i) its robustness to parameter modification and model unsureness, ii) low computational complexity, and iii) high dynamic response and control stability.