A celebrated and controversial hypothesis suggests that some biological systems-parts, aspects, or groups of them-may extract important functional benefits from operating at the edge of instability, halfway between order and disorder, i.e., in the vicinity of the critical point of a phase transition. Criticality has been argued to provide biological systems with an optimal balance between robustness against perturbations and flexibility to adapt to changing conditions as well as to confer on them optimal computational capabilities, large dynamical repertoires, unparalleled sensitivity to stimuli, etc. Criticality, with its concomitant scale invariance, can be conjectured to emerge in living systems as the result of adaptive and evolutionary processes that, for reasons to be fully elucidated, select for it as a template upon which further layers of complexity can rest. This hypothesis is suggestive as it proposes that criticality could constitute a general and common organizing strategy in biology stemming from the physics of phase transitions. However, despite its implications, this is still in its infancy state as a well-founded theory and, as such, it has elicited some skepticism. From the experimental side, the advent of high-throughput technologies has created new prospects in the exploration of biological systems, and empirical evidence in favor of criticality has proliferated, with examples ranging from endogenous brain activity and gene-expression patterns to flocks of birds and insect-colony foraging, to name but a few. Some pieces of evidence are quite remarkable, while in some other cases empirical data are limited, incomplete, or not fully convincing. More stringent experimental setups and theoretical analyses are certainly needed to fully clarify the picture. In any case, the time seems ripe for bridging the gap between this theoretical conjecture and its empirical validation. Given the profound implications of shedding light on this issue, it is both pertinent and timely to review the state of the art and to discuss future strategies and perspectives.