Efficient terahertz generation and detection are a key prerequisite for high performance terahertz systems. Major advancements in realizing efficient terahertz emitters and detectors were enabled through photonics-driven semiconductor devices, thanks to the extremely wide bandwidth available at optical frequencies. Through the efficient generation and ultrafast transport of charge carriers within a photo-absorbing semiconductor material, terahertz frequency components are created from the mixing products of the optical frequency components that drive the terahertz device – a process usually referred to as photomixing. The created terahertz frequency components, which are in the physical form of oscillating carrier concentrations, can feed a terahertz antenna and get radiated in case of a terahertz emitter, or mix with an incoming terahertz wave to down-convert to DC or to a low frequency photocurrent in case of a terahertz detector. Realizing terahertz photoconductors typically relies on short-carrier-lifetime semiconductors as the photo-absorbing material, where photocarriers are quickly trapped within one picosecond or less after generation, leading to ultrafast carrier dynamics that facilitates high-frequency device operation. However, while enabling broadband operation, a sub-picosecond lifetime of the photocarriers results in a substantial loss of photoconductive gain and optical responsivity. In addition, growth of short-carrier-lifetime semiconductors in many cases relies on the use of rare elements and non-standard processes with limited accessibility. Therefore, there is a strong motivation to explore and develop alternative techniques for realizing terahertz photomixers that do not rely on these defect-introduced short-carrier-lifetime semiconductors. This review will provide an overview of several promising approaches to realize terahertz emitters and detectors without short-carrier-lifetime semiconductors. These novel approaches utilize p-i-n diode junctions, plasmonic nanostructures, ultrafast spintronics, and low-dimensional materials to offer ultrafast carrier response. These innovative directions have great potentials for extending the applicability and accessibility of the terahertz spectrum for a wide range of applications.