Quantum-cascade vertical-external-cavity surface-emitting-laser (QC-VECSEL) is a recently developed compact and coherent source of THz radiation which has demonstrated excellent beam quality and scalable high-power. The key component of the QC-VECSEL is an amplifying reflectarray metasurface made up of an array of sub-wavelength metal-metal waveguides loaded with quantum-cascade (GaAs/AlGaAs) laser gain material. To further the usefulness of this technology for many applications, including spectroscopy, heterodyne detection, and multispectral imaging, broadband and tunable THz QCLs are required. In this work, I investigate the feasibility of two techniques for tuning THz metasurface-based QCLs. First, A Littrow metasurface external cavity laser (ECL) is modeled and studied. We also propose and evaluate a novel method to implement Littrow ECL based upon blazed metasurface gratings. Electromagnetic simulations show that these metasurfaces can provide up to 15% fractional tunability around the center frequency of the laser at 3.3 THz. Preliminary results on several active resonant-phonon quantum-cascade materials are also obtained. Current progress on actual fabrication and device testing is reported.