Life presents us with bewildering phenomenology, from robust self-replication and morphogenesis, to learning, adaptation, and evolution. These phenomena are collective and typically carry no precedent in the inanimate world, which presents an exciting opportunity in the search for new emergent physics. Modern experimental methods offer increasingly high-resolution and large-scale data on the inner workings of biology, making conceivable the establishment of precise theories about the organization of living systems. As first steps towards this lofty and long-term goal, we need principles to define the most biologically relevant features in high-dimensional datasets, as well as tools to identify them and constrain theory. Motivated by the successes of many-body theory in physics, we examine how the renormalization group (RG) and information bottleneck (IB), two paradigmatic coarse-graining approaches, may contribute to the search for simplifying structure in large-scale biology. First, to explore how top-down and bottom-up coarse-graining might be reconciled, we demonstrate a formal theoretical connection between IB and RG. We find that the choice of relevance variable in IB determines the collective variables and their order of elimination in the RG scheme, suggesting IB can be used to select a notion of ‘large scale’ structure, such as a particular biological function. One especially exciting application of this idea may be to use it as a bridge, revealing how effective models in the language of RG can be read out of IB analyses on biological data. Next, prompted by multi-functionality in biology, we examine the idea that a given system might have multiple notions of large scale structure. We construct a simple model which exhibits this property, in that its correlations are best described in terms of two coexisting but independent RG flows, each coarse-graining with respect to a different collective basis. The failure of RG to predict large-scale correlations in a certain phase of this model points to a potential pitfall in interpreting maximum-entropy models of biological data as many-body systems. Finally, we turn our attention to real biological systems, and use IB to coarse-grain data taken from a large population of neurons in the salamander retina. By optimizing collective variables to predict future responses, we identify features in the retinal code that may enable downstream visual prediction. We also reveal that the encoding of predictive information in the retina becomes increasingly collective at long times, accompanied by a shift in the most relevant collective variables. This highlights the importance of adapting coarse-graining to function in biology.