This work addresses challenges in the emerging field of microlength scale radiative and conductive heat transfer in solids and recommends specific directions of future research. Microlength scale heat transfer involves thermal energy transport processes in which heat carrier characteristic lengths become comparable to each other or the characteristic device dimension. Identification of these characteristic lengths leads to the definition of different microscale heat transfer regimes. A review of the theoretical bases describing heat transfer in each regime is followed by a discussion of the obstacles confronted in current research. Engineering challenges are illustrated with the applications of microscale heat transfer in cryogenic systems, material processing, and electronic, optical, and optoelectronic devices. The experimental difficulties discussed have hampered the development of microscale heat transfer research and deserve great efforts to overcome them.