Photoluminescence including fluorescence plays a great role in a wide variety of applications from biomedical sensing and imaging to optoelectronics. Therefore, the enhancement and control of photoluminescence has immense impact on both fundamental scientific research and aforementioned applications. Among various nanophotonic schemes and nanostructures to enhance the photoluminescence, we focus on a certain type of nanostructures, hyperbolic metamaterials (HMMs). HMMs are highly anisotropic metamaterials, which produce intense localized electric fields. Therefore, HMMs naturally boost photoluminescence from dye molecules, quantum dots, nitrogen-vacancy centers in diamonds, perovskites and transition metal dichalcogenides. We provide an overview of various configurations of HMMs, including metal-dielectric multilayers, trenches, metallic nanowires, and cavity structures fabricated with the use of noble metals, transparent conductive oxides, and refractory metals as plasmonic elements. We also discuss lasing action realized with HMMs.