Laser beam machining (LBM) has proven its applications and advantages over almost all the range of engineering materials. It offers its competences from macro-machining to micro- and nano-machining of simple-to-complex shapes. The hybrid approaches in laser ablation have demonstrated much improved results in terms of material removal rate, surface integrity, geometrical tolerances, thermal damage, metallurgical alterations, and many more. The flipside of LBM is the existence of universal problems associated with its thermal ablation mechanism. In order to alleviate or reduce the inherent problems of LBM, a massive research has been done during the past decade in order to build a relatively new route of laser-hybrid processes. This paper reviews the research work carried out so far in the area of LBM and its hybrid processes for different materials and shapes. The article also highlights the research gaps and future research directions in the context of laser and laser-hybrid ablation.