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The development of high performance heterostructure transistors is essential for emerging opto-electronic integrated circuits (OEICs) and monolithic microwave integrated circuits (MMICs). Applications for OEICs and MMICs include the rapidly growing telecommunications and personal communications markets. The key to successful OEIC and MMIC chip sets is the development of high performance, cost-effective technologies. In this work, several different transistor structures are investigated to determine the potential for high speed performance and the physical mechanisms controlling the ultimate device operation. A cryogenic vacuum microwave measurement system has been developed to study the high speed operation of modulation doped field-effect transistors (MODFETs), doped channel metal insulator field-effect transistors (MISFETs), and metal semiconductor field-effect transistors (MESFETs). This study has concluded that the high field velocity and not the low field mobility is what controls high frequency operation of GaAs based field-effect transistors. Both Al$sb{rm x}$Ga$sb{rm 1-x}$As/GaAs and InP/In$sb{rm y}$Ga$sb{rm 1-y}$As heterostructure bipolar transistors (HBTs) have also been studied at reduced lattice temperatures to understand the role of diffusive transport in the Al$sb{rm x}$Ga$sb{rm 1-x}$As/GaAs HBT and nonequilibrium transport in the InP/In$sb{rm y}$Ga$sb{rm 1-y}$As HBT. It is shown that drift/diffusion formulation must be modified to accurately estimate the base delay time in the conventional Al$sb{rm x}$Ga$sb{rm 1-x}$As/GaAs HBT. The reduced lattice temperature operation of the InP/In$sb{rm y}$Ga$sb{rm 1-y}$As HBT demonstrates extreme nonequilibrium transport in the neutral base and collector space charge region with current gain cut-off frequency exceeding 300 GHz, which is the fastest reported transistor to date. Finally, the MODFET has been investigated as a three-terminal negative differential resistance (NDR) transistor. The existence of real space transfer is confirmed by analyzing the dc and microwave characteristics of the MODFET. The data are shown to correlate very well with the theoretical predictions of tunneling real space transfer between the channel and donor layer.