The chromosphere is one of the most complex and dynamic layers of the solar atmosphere. The dynamic phenomena occur on different spatial and temporal scales, not only in active regions but also in the so-called quiet Sun. In this paper we review recent advances in our understanding of these phenomena that stem from the analysis of observations with the Atacama Large Millimeter/submillimeter Array (ALMA). The unprecedented sensitivity as well as spatial and temporal resolution of ALMA at millimeter wavelengths have advanced the study of diverse phenomena such as chromospheric p-mode-like and high-frequency oscillations, as well as small-scale, weak episodes of energy release, including shock waves. We review the most important results of these studies by highlighting the new aspects of the phenomena that have revealed as well as the new questions and challenges that have generated.