The grating-gate plasmonic crystal system represents a compelling arena for investigating strong light-matter interactions and diverse plasmon resonances. This study reviews the recent discovery of two distinctive terahertz phases of AlGaN/GaN plasmonic crystals that arise from varying the modulation of a two-dimensional electron density beneath the metallic gratings: the delocalized phase at weak modulation and the localized phase at strong modulation. Notably, we delve into an impact of the grating filling factor on the electrically driven transition between these phases. Our findings underscore the critical role of specific metal grating geometry parameters in facilitating this transition. Moreover, we explore the potential of utilizing graphene-based gratings as alternatives to metallic gratings. Through the integration of graphene, grown by Chemical Vapor Deposition method on copper foil and then transferred to the high electron mobility AlGaN/GaN heterostructures, we achieve an effective modulation of broadband absorption by free charge carriers within the 0.5–6 THz range via electrical biasing of the graphene electrode. However, while this approach successfully modulates absorption in a wide THz range, it does not elicit plasmon resonances within the graphene-based grating-gate plasmonic crystals. This intriguing observation poses a significant unresolved question warranting further theoretical and experimental exploration in subsequent studies.