Despite significant advances in cloud physics, many problems exist in the state-of-the-art microphysical cloud modeling. The progress is hampered by (1) many remaining gaps and uncertainties in our knowledge of cloud microphysics and (2) limitations of numerical approaches in representing some of known microphysical processes. In this paper, we attempt to give an assessment of several important problems of warm and ice microphysics and model limitations and identify areas where improvements are most urgently needed. Because of the complexity and broadness of the subject, the review does not offer an exhausted analysis of the field or provide solutions for all discussed problems. We are concerned with the spectral (bin) microphysical approach, which does not restrict the particle size spectra to any particular shape and, therefore, claims to reproduce formation of size spectra of cloud particles.