Electronic transport in semiconductors that possess high internal spontaneous and piezoelectric polarization opens up a new field of pyroelectronics and pyrosensors. The pyroelectric character of group-III-nitrides with wurtzite crystal structure yields a novel degree of freedom in designing and tailoring devices for modern micro- and nanoelectronic applications. Furthermore spontaneous and piezoelectric polarization induced surface and interface charges can be used to develop very sensitive but robust sensors for the detection of ions, gases, polar liquids and UV-light. We present a review of both theoretical and experimental studies of spontaneous and piezoelectric polarization present in AlGaN/GaN heterostructures as well as the electronic transport properties of polarization induced two-dimensional electron gases which are formed at the AlGaN/GaN interface due to the difference in the total polarization of two adjacent III-nitride layers. We demonstrate that the two-dimensional electron gases (2DEGs) achieved without modulation doping are very suitable as channel of high electron mobility transistors optimally suited for high power and high frequency applications. In addition we review recent achievements concerning optical and chemical sensor applications of undoped AlGaN/GaN heterostructure field effect transistor devices. We summarize experimental results on the optical effects of AlGaN based heterostructures for highly selective detection of UV-light, the sensitivity of GaN Schottky diodes and gas sensitive field effect transistors for the detection of hydrogen and hydrogen containing gases as well as the performance of AlGaN/GaN based ion sensitive field effect transistors for highly sensitive pH measurements in electrolyte solutions.