Abstract: We present recent advances in the development of NbN hot-electron bolometric (HEB) mixers for flying terahertz heterodyne receivers. Three important issues have been addressed: the quality of the source NbN films, the effect of the bolometer size on the spectral properties of different planar feed antennas, and the local oscillator (LO) power required for optimal operation of the mixer. Studies of the NbN films with an atomic force microscope indicated a surface structure that may affect the performance of the smallest mixers. Measured spectral gain and noise temperature suggest that at frequencies above 2.5 THz the spiral feed provides better overall performance than the double-slot feed. Direct measurements of the optimal LO power support earlier estimates made in the framework of the uniform mixer model.