Due to the significant development in the field of power electronics over the last decade, Permanent Magnet Synchronous Machines (PMSM) are widely used in variable frequency drives, ranging from small-power (couple 100 Watts) servo drives to higher power (10-100 kW) applications. Their life-time is longer and their efficiency is better compared to the brushed DC motors, and their power density is higher than that of the Induction Motors. Permanent Magnet Synchronous Machines are used more frequently in vehicles as well, both in servo systems (e.g. power steering) and in the powertrain in case of hybrid or electrical vehicles. To achieve proper operation of the synchronous machines, usually closed loop vector control is used. The aim of the project is to investigate two of most popular vector control methods, which can be used for controlling synchronous machines as well. These are the Direct Torque Control and Field Oriented Control. In the case of Field Oriented Control the stator currents are transformed to the reference frame attached to the rotor, and the calculated d and q components of the current vector, which are the flux and torque producing components, are controlled using linear controllers. The switching signals are generated using Pulse Width Modulation. In the case of Direct Torque Control the control of the stator current vector is achieved by controlling the stator flux vector. In this case, the switching signals are established using hysteresis comparators and a switching table. The paper presents the differential equations of the machine. With these the corresponding transfer functions are derived and used for the controller design. Simulations for both controller methods are shown, which were developed in Matlab/Simulink environment. Besides the simulations the hardware implementation of the algorithms is also presented. Using the measurement and simulation results the two methods are compared and conclusions are also drawn regarding their application possibilities in electric powertrains. In the paper other control strategies are also mentioned and future improvement possibilities are listed.