Researches on the interactions between drifting carrier plasma waves and electromagnetic waves were intensively studied theoretically and experimentally in 1960s to 1990s but faded out with inconclusive results. This study presents a series of fundamental works carried out by our group in order to re-evaluate the possibility of realizing a solid-state amplifier operating in THz region based on the drifting plasma wave interactions. Firstly, we described a new method to analyze the properties of semiconductor drifting plasma in a semiconductor-insulator structure based on the Transverse Magnetic (TM) mode analysis. The components of waves, the electromagnetic fields and the ω- and k- dependent effective permittivity which are used to describe the dielectric response of the semiconductor plasma to the TM surface wave excitation are derived. Then, the properties of semiconductor drifting plasma in a two-dimensional electron gas (2DEG) structure using the developed TM mode analysis are presented. Here, the electromagnetic fields and the ω- and k- dependent effective permittivity of the 2DEG drifting plasma are also determined. The analyzed device structure and formulation procedures to explain the interactions between drifting plasma waves in semiconductor and electromagnetic waves propagating through the interdigital slow-wave structure is then presented. Next, some preliminary experimental studies of plasma wave interactions using interdigital-gated n-AlGaAs/GaAs high-electron-mobility-structure carried out are presented. Finally, we concluded the findings or contributions of our work and some remarks for future research.