The presence of interconnected processes taking place at multiple temporal scales is one of the fundamental features of biochemistry, neural networks, ecological communities, and many other complex systems. A key feature is that these processes may interact both directly and indirectly with one another, and such interactions across timescales may not be pairwise. This makes understanding the relationship between their components a formidable challenge. In this talk, we will first focus on how the different timescales associated with each layer impact their effective couplings. We derive a general decomposition of the joint probability distribution that is valid for any set of dynamical processes, and we introduce the general principles governing how information propagates across timescales. In doing so, we elucidate the interplay between mutual information and causality in multiscale systems. We show how this information structure can exploited to study minimal models of biochemical signaling networks and to understand the relations between their fundamental components. Further, we apply our framework to characterize the effective dependencies induced by changing environmental conditions in coupled stochastic processes. Finally, we outline a promising future perspective where we introduce the concept of information precision, which incorporates the variance of mutual information along stochastic trajectories.