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The Sun exhibits a rich variety of periodic phenomena. The most prominent among them is the 11-year sunspot cycle. However, reconstructions of solar activity over centuries reveal that the amplitude of this cycle itself varies on longer, often irregular, timescales. These long-term variations, referred to as supradecadal modulation, remain poorly understood, with several competing hypotheses under debate. In this talk, I will explore the role of stochastic forcing as a potential driver of such modulation. I will also discuss periodic flows on shorter timescales — on the order of months — recently discovered in solar surface velocity fields. These periodic flows, known as solar inertial modes, exhibit evident variability over the solar cycle and are sensitive to internal solar properties that also influence the solar dynamo. Understanding these modes offers a new window into the solar interior. I will present the current state of their theoretical modelling and highlight how assumptions in the continuity equation can significantly affect their interpretation. Together, these perspectives offer valuable insights into the dynamics underlying solar variability. |