The invention of lasers 60 years ago is one of the greatest breakthroughs in modern optics. Throughout the years, lasers have enabled major scientific and technological advancements, and have been exploited in numerous applications due to their advantages such as high brightness and high coherence. However, the high spatial coherence of laser illumination is not always desirable, as it can cause adverse artifacts such as speckle noise in imaging applications. To reduce the spatial coherence of a laser, novel cavity geometries and alternative feedback mechanisms have been developed. By tailoring the spatial and spectral properties of cavity resonances, the number of lasing modes, the emission profiles and the coherence properties can be controlled. This technical review presents an overview of such unconventional, complex lasers, with a focus on their spatial coherence properties. Laser coherence control not only provides an efficient means for eliminating coherent artifacts, but also enables new applications.