III-N family of materials has offered multiple groundbreaking technologies in the field of optoelectronics and high-power radio-frequency (RF) devices. Blue light-emitting diodes (LEDs) have revolutionized low-energy lighting. Gallium nitride (GaN) RF market is projected to reach 2 billion US\$ by 2025, driven by the defense and telecom applications (namely, 5G). Since a few years, a relatively new field of GaN power electronics is actively growing and just entering the consumer market. The main applications are fast smartphone chargers, automotive, data center, and aerospace. GaN high-electron-mobility (HEM) transistor (HEMT) is the major GaN-based power device commercially available nowadays. The high breakdown field of GaN together with the enhanced mobility offered by the high-electron-mobility heterostructure offers numerous advantages over existing Si-based devices. GaN HEMTs are significantly smaller than their Si counterparts and, thus, switch faster. Increased switching frequency allows to drastically reduce the converter size as well as switching power loss. Thus, GaN-based power devices pave the way to future efficient power conversion technologies. Multi-channel III-N heterostructures are the next step towards the ultimate optimization of a GaN HEMT. By vertically stacking multiple HEM channels one can significantly reduce the ON-resistance of the devices without sacrificing voltage blocking performance, thus, surpassing the fundamental trade-off between ON-resistance and breakdown voltage. In this thesis, we present a detailed analysis of the design principles of multi-channel high electron mobility heterostructures. We provide analytical tools to fine-tune carrier concentrations in each of the multiple channels to achieve the optimal carrier distribution profile for a given application. Based on the analysis presented, we develop a novel device concept - intrinsic polarization super-junction (iPSJ) diode. We demonstrate numerically and analytically that single-channel iPSJ fully decouples the ON-state conductivity from the OFF-state, alleviating the trade-off between the ON-resistance and breakdown voltage. Further, we apply the same concept to a multi-channel (MC) stack. We propose MC-iPSJ devices that surpass the existing GaN HEMT material limit. The technology presented offers a robust platform compatible with current commercial fabrication techniques. The multi-channel requires gate and access regions patterned with nanowires to ensure efficient depletion by the gate and optimal field distribution in the access region. We perform a thorough experimental and analytical study of electrical properties of top-down etched GaN HEMT nanowires that shed light on the strategies to achieve normally-off behavior and optimize the passivation of tri-gated HEMTs. Finally, we explore an alternative gating technique for the multi-channel stack-in-plane gate (IPG), offering advantages in terms of gate capacitance for potential RF applications. We experimentally demonstrate a multi-channel in-plane gate transistor being 3.5-times more conductive than its single-channel counterpart advancing the state-of-the-art. This thesis presents a complete overall study of multi-channel heterostructures, along with specific field management and gating techniques required for this new technology. The experimental results and analytical tools presented provide a solid basis for the future optimization of MC-HEMTs.