Sensorimotor predictions are essential for adaptive behavior. In natural environments, events that demand sensorimotor predictions unfold across many timescales, and corresponding temporal predictions (either explicit or implicit) should therefore emerge in brain dynamics. Neuronal oscillations are scalespecific processes found in several frequency bands. They underlie periodicity in sensorimotor processing and can represent temporal predictions via their phase dynamics. These processes build upon endogenous neural rhythmicity and adapt in response to exogenous timing demands. While much of the research on periodicity in neural processing has focused on subsecond oscillations, these fast-scale rhythms are in fact paralleled by critical-like, scale-free dynamics and fluctuations of brain activity at various timescales, ranging from seconds to hundreds of seconds. In this review, we put forth a framework positing that critical brain dynamics are essential for the role of neuronal oscillations in timing and that cross-frequency coupling flexibly organizes neuronal processing across multiple frequencies. Critical-like Multiscale Brain Oscillations for Processing a Critical-like Multiscale Environment? Perception and action in natural environments necessitate interplay among representations of past events, the current state, as well as predictions of both future events and the consequences of our own actions across a continuum of vastly different timescales. Notably, natural visual [1] and auditory [2] scenes are characteristically scale-free and arrhythmic signals with power-law scaling behavior (Box 1 and Figure 1A-C). Such lack of scaling or periodicities is perhaps not too surprising, considering that many aspects of our environment are ongoing processes involving nonlinear interactions among many agents, or are products of such processes, and thereby encompass complex or 'critical' spatiotemporal dynamics [3]. Critical dynamics appear in systems poised at a transition between two phases, and such systems are characterized by stochastic fractal-like architectures, power-law correlations, and rapid intermittent state transitions [3,4]. However, in many real-world settings scale-free environmental contexts are accompanied by distinct scale-specific phenomena (i.e., periodic or quasiperiodic signals; Box 1). Such scale-specific components arise both from artificial sources and from biological systems, for instance through phenomena with rhythmic components, such as gait and production of speech and music (Figure 1C-E). What are the neural processes that facilitate effective perception, cognition, and action in environments that consist of both scale-free and scale-specific temporal structures? The range of behaviorally relevant environmental temporal scales is well paralleled by the spectrum of Highlights Neuronal oscillations in ongoing brain activity adapt to behaviorally relevant sensorimotor rhythmicities by phase prediction and entrainment. Neuronal oscillations also endogenously impose rhythmicity on perceptual...