Next-generation wireless networks are facing spectrum shortage challenges, mainly due to, among other factors, the projected massive numbers of IoT connections and the emerging bandwidth-hungry applications that such networks ought to serve. Spectrum is scarce and expensive, and therefore, it is of crucial importance to devise dynamic and flexible spectrum access policies and techniques that yield optimal usage of such a precious resource. A new trend recently being adopted as a key solution to this spectrum scarcity challenge is to exploit higher frequency bands, namely mmWave bands, that were considered impractical few years ago, but are now becoming feasible due to recent advances in electronics. Though, fortunately, spectrum regulatory bodies have responded by allowing the use of new bands in the mmWave frequencies, much work still needs to be done to benefit from such new spectra. In this paper, we discuss some key spectrum management challenges that pertain to dynamic spectrum access at the mmWave frequencies, which need to be overcome in order to promote dynamic spectrum sharing at these mmWave bands. We also propose new techniques that enable efficient dynamic spectrum sharing at the mmWave bands by addressing some of the discussed challenges, and highlight open research challenges that still need to be addressed to fully unleash the potential of dynamic spectrum sharing at mmWave bands.