The quantum cascade laser (QCL) has been central to the development of terahertz (THz) science and technology in the last decade, thanks to its electronic and optical properties, which can be accurately tailored with quantum and photonic engineering. Control over the spatial and spectral features of THz QCL radiation has been addressed with different solutions, exploiting periodic structures such as edge-emitting 3rd-order distributed feedback lasers, plasmonic lasers, and one dimensional (1D) or two-dimensional (2D) photonic crystals. Novel resonators exploiting aperiodic photonic architectures recently emerged as a versatile approach to engineer the emission of THz QCLs, circumventing the power extraction issues of periodic resonators. Here, we report on the development of 1D and 2D THz QCL resonators providing a combination of high output power, controlled beam shaping and stable continuous wave (CW) operation. We devised a laterally corrugated wire laser with a top extraction hole array. The distinct periodicities of the lateral corrugation and the top hole array allow separate control of light feedback and extraction, optimizing the power output (42 mW in pulsed regime), slope efficiency (250 mW/A) and beam divergence (10°). Stable single-mode emission was achieved with a maximum CW power output of 6 mW. We furthermore demonstrate the first electrically pumped CW random THz lasers reaching a maximum peak power of 21 mW and a CW power of 1.7 mW with multimode emission over a 430 GHz-bandwidth. Using an external coupled cavity, a continuous tuning of 11 GHz and of 20 GHz with modehopping were demonstrated.