Achieving both high power and high-quality beam pattern has been a longstanding challenge for terahertz (THz) quantum-cascade (QC) lasers largely due to their use of subwavelength metallic waveguides. Recently, the vertical-external-cavity surface-emitting laser (VECSEL) concept was demonstrated for the first time in the THz range and for a QC-laser. This is enabled by the development of an amplifying metasurface reflector capable of coupling incident free-space THz radiation to the QC-laser material such that it is amplified and reradiated. The THz metasurface QC-VECSEL initiates a new approach for making QC-lasers with high power and excellent beam pattern. Furthermore, the ability to engineer the electromagnetic phase, amplitude, and polarization response of the metasurface enables lasers with new functionality. This paper provides an overview of the fundamental theory, design considerations, and recent results for high-performance THz QC-VECSELs.