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.

半个多世纪以来，人们一直在太阳大气层中观察到波动和振荡。虽然这种现象很容易在整个电磁频谱中观察到，从无线电到伽马射线源，但波在向太阳日冕最外端提供能量的过程中的潜在作用尚未被发现。特别令人感兴趣的是较低的太阳大气层，包括光球层和色球层，因为这些区域拥有强大的磁通量束的立足点，能够引导太阳表面向上的振荡运动。因此，许多当前和下一代的地面和星载观测设施都将注意力集中在太阳低层大气的这些脆弱层上，试图在尽可能高的空间和时间尺度上进行研究，负责高能波现象的产生、传播和最终消散的机制。在这里，我们提出了一个双重回顾，旨在概述太阳物理学界目前可以使用的波动分析技术，并强调过去十年取得的科学进步。重要的是，虽然许多开创性的研究将解决和回答太阳物理学的关键问题，但其研究的前沿性质自然会提出更突出的观测和/或理论问题，需要后续的后续工作。这不仅是可以预料的，而且应该被视为对我们目前所处的快速发现时代的提醒。我们将强调这些悬而未决的问题，并提出太阳物理学界在未来几年和几十年内解决这些问题的方法来。