The outstanding material properties of III-Nitride semiconductors, has prompted intense research efforts in order to engineer resonant tunneling transport within this revolutionary family of wide-bandgap semiconductors. From resonant tunneling diode (RTD) oscillators to quantum cascade lasers (QCLs), III-Nitride heterostructures hold the promise for the realization of high-power ultra-fast sources of terahertz (THz) radiation. However, despite the considerable efforts over last two decades, it is only during the last three years that room temperature resonant tunneling transport has been demonstrated within the III-Nitride family of semiconductors. In this paper we present an overview of our current understanding of resonant tunneling transport in polar heterostructures. In particular we focus on double-barrier III-Nitride RTDs which represents the simplest device in which the dramatic effects of the internal polarization fields can be studied. Tunneling transport within III-heterostructures is strongly influenced by the presence of the intense spontaneous and piezoelectric polarization fields which result from the non-centrosymmetric crystal structure of III-Nitride semiconductors. Advances in heterostructure design, epitaxial growth and device fabrication have led to the first unequivocal demonstration of robust and reliable negative differential conductance. which has been employed for the generation of microwave power from III-Nitride RTD oscillator. These significant advances allowed us to shed light into the physics of resonant tunneling transport in polar semiconductors which had remained hidden until now.