Random Lasers (RLs) and Random Fiber Lasers (RFLs) have been the subject of intense research since their first experimental demonstration in 1994 and 2007, respectively. These low coherence light sources rely on multiple scattering of light to provide optical feedback in a medium combining a properly excited gain material and a scattering disordered structure. It is the feedback mechanism which makes RLs/RFLs quite different from conventional lasers, with the later relying on an optical cavity usually formed by two static mirrors. This characteristic makes the RLs and RFLs devices to become cavityless, although not modeless, and present features of complex systems, whose statistics of intensity fluctuations are quite relevant. In addition, RLs can be designed in three-dimensional (3D) geometry, typically powders or colloids, in two-dimensional (2D) geometries, such as planar waveguides or thin-films, and one-dimensional (1D or quasi-1D) geometry, generally in optical fibers, known as the RFLs. The advantage of 1D geometry is the inherent directionality of the RFL emission, which otherwise is multidirectional in 3D geometry. In this review paper, we initially describe the basic theoretical framework supporting laser emission due to feedback in disordered structures. We then provide an updated vision of the types of RLs and RFLs that have been demonstrated and reported, from dyes solutions embedded with nano/submicron-scatterers composites to rare-earth doped micro or nanocrystals and random fiber Bragg gratings as the scattering structure. The influence of optical processes due to second-, third- and high-order nonlinearities on the intensity behavior of RLs are discussed. Subsequently, we review multidisciplinary studies that lead to the classification of RLs as complex systems exhibiting turbulence-like characteristics, photonic phase-transitions presenting replica symmetry breaking and intensity fluctuations satisfying Lévy-like statistics, and the so-called Floquet phase. Furthermore, we also highlight technological applications that include
s sensing, optical amplification, and biomedical imaging. The review concludes pointing out potential directions in basic and applied research in the field of RL and RFL.