With higher frequencies and broader spectrum than conventional frequency bands, the millimeter-wave (mmWave) band is suitable for next-generation wireless networks featuring short-distance high-rate communications. As a newcomer, mmWaves are expected to have the backward compatibility with existing services and collaborate with other technologies in order to enhance system performances. Therefore, the coexistence issues become an essential topic for next-generation wireless communications. In this paper, we systematically review the coexistence issues of broadband mmWave communications and their corresponding solutions proposed in the literature, helping shed light on the insights of the mmWave design. Particularly, the works surveyed in this paper can be classified into four categories: coexistence with microwave communications, coexistence with fixed services, coexistence with non-orthogonal multiple access (NOMA), and other coexistence issues. Results of numerical evaluations inspired by the literature are presented for a deeper analysis. We also point out some challenges and future directions for each category as a roadmap to further investigate the coexistence issues of broadband mmWave communications.