Waves and oscillations have been observed in the Sun’s atmosphere for over half a century. While such phenomena have readily been observed across the entire electromagnetic spectrum, spanning radio to gamma-ray sources, the underlying role of waves in the supply of energy to the outermost extremities of the Sun’s corona has yet to be uncovered. Of particular interest is the lower solar atmosphere, including the photosphere and chromosphere, since these regions harbor the footpoints of powerful magnetic flux bundles that are able to guide oscillatory motion upwards from the solar surface. As a result, many of the current- and next-generation ground-based and space-borne observing facilities are focusing their attention on these tenuous layers of the lower solar atmosphere in an attempt to study, at the highest spatial and temporal scales possible, the mechanisms responsible for the generation, propagation, and ultimate dissipation of energetic wave phenomena. Here, we present a two-fold review that is designed to overview both the wave analyses techniques the solar physics community currently have at their disposal, as well as highlight scientific advancements made over the last decade. Importantly, while many ground-breaking studies will address and answer key problems in solar physics, the cutting-edge nature of their investigations will naturally pose yet more outstanding observational and/or theoretical questions that require subsequent follow-up work. This is not only to be expected, but should be embraced as a reminder of the era of rapid discovery we currently find ourselves in. We will highlight these open questions and suggest ways in which the solar physics community can address these in the years and decades to come.

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.