Vortex lasers are the optical beams possessing intensity center of zero and orbital angular momentum. In recent years, generation of the vortex lasers and chirality-control techniques get more and more attention due to their unique applications in particle manipulation, information communication and super-resolution imaging, etc. The techniques of the vortex lasers directly generated from solid-state cavities are summarized, and the corresponding merits and drawbacks are respectively analyzed. Then, the optical field distributions of opposite-handedness vortex lasers in the standing wave cavity are derived through theoretical simulation. Finally, based on the field distribution characteristics of vortex lasers with different handednesses, the handedness-control techniques for vortex lasers directly generated are reviewed, and their principles and technical proposals are further compared and analyzed.