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Regime shifts in ecosystems are typically understood to be abrupt global transitions from one stable state to an alternative stable state, induced by slow environmental changes or global disturbances. This is especially relevant to drylands, where desertification is a major concern. However, spatially extended ecosystems, and dryland vegetation systems in particular, often exhibit patterned states, which allow for more complex dynamics to take place. Periodic patterns can have many different wavelengths, implying different length-scales of patchy vegetation. Further, a bistability of a patterned state and a uniform state can lead to a multitude of stable hybrid states, with small domains of one state embedded in the other state. The response of the system to local disturbances or change in global parameters in these systems can lead to gradual regime shifts, involving the expansion of alternative-state domains by front propagation, rather than a global collapse. Moreover, a regime of periodic perturbations can give rise to step-like gradual shifts with extended pauses at these states. The implications of different forms of patterned states on the dynamics of the system will be discussed, with three points in mind: The question of desertification as a front propagation process, the effect of local disturbances on the system, and a specific case study on the dynamics of fairy circles in Namibia as a concrete example.