Laser forming is an emerging manufacturing process capable of producing either uncomplicated and complicated shapes by employing a concentrated heating source. The heat source movement creates local softening, and a plastic strain will be induced during the rise of temperature and the subsequent cooling. This contactless forming process may be used for the simple bending of sheets and tubes or fabrication of doubly-curved parts. Different studies have been carried out over recent years to understand the mechanism of forming and predicting the bending angle. The analysis of process parameters and search for optimized manufacturing conditions are among the most discussed topics. This review describes the main recent findings in the laser forming of single and multilayer sheets, composite and fiber-metal laminate plates, force assisted laser bending, tube bending by laser beam, the optimization technique implemented for process parameters selection and control, doubly-curved parts, and the analytical solutions in laser bending. The main focus is set to the researches published since 2015.