Gallium nitride (GaN) high-electron-mobility transistors (HEMTs) have become the leading technology for high-power and high-frequency electronics. However, further performance scaling of conventional AlGaN/GaN HEMTs is increasingly limited by thermal dissipation and parasitic constraints. The poor thermal boundary conductance at the heteroepitaxial interface and the thick, defect-rich buffer layers required to accommodate lattice mismatch severely restrict heat removal and degrade device reliability under high-power operation. This dissertation establishes single-crystal aluminum nitride (AlN) as a new platform for GaN-based high-speed, high-power transistors, eliminating the thermal bottleneck inherent to conventional heteroepitaxial structures. A series of pseudomorphic GaN/AlN heterostructure HEMTs (XHEMTs) were designed, fabricated, and characterized to explore the performance of the GaN material system grown on lattice-matched AlN substrates. The work presents undoped and silicon δ-doped metal-polar AlN/GaN/AlN XHEMTs, and N-polar GaN/Al(Ga)N XHEMT architectures on bulk AlN substrates, supported by systematic studies of surface passivation, ohmic contact formation, RF dispersion, and thermal management. The exploration of undoped metal-polar XHEMTs established the fundamental performance limits of the pseudomorphic GaN channel on AlN. The first-generation devices exhibited strong potential for RF amplification, as evidenced by excellent DC and small-signal performance, but their output power was limited by severe charge trapping and current collapse during large-signal operation. Building on these initial results, a fabrication process tailored to the XHEMT heterostructure was developed, incorporating improved regrown ohmic contacts, robust T-shaped gate profiles, and high-quality dielectric passivation. These refinements substantially enhanced device uniformity and power performance, yet the ultimate limitation was traced to an intrinsic feature of the GaN/AlN system — the formation of a polarization-induced two-dimensional hole gas (2DHG) at the bottom interface. To address this fundamental constraint, silicon δ-doping was introduced as a structural modification to neutralize the negative polarization charge and suppress the 2DHG, resulting in reduced RF dispersion and enhanced efficiency. In parallel, thermal analysis revealed the superior heat-spreading capability of metal-polar XHEMTs on AlN, underscoring its advantage for high-power operation. The final phase of this work investigated N-polar Al(Ga)N/AlN XHEMTs and polarization-doped field-effect transistors (PolFETs) on single-crystal AlN substrates, extending the AlN platform to encompass both polarities of the wafer. These demonstrations underscore the versatility of the AlN substrate in supporting complementary device architectures — metal-polar and N-polar— each offering a unique set of electrical, structural, and thermal advantages, reinforcing the promise of AlN as a unified foundation for next-generation wide-bandgap electronics.