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Fireflies offer a unique and rare glimpse into animal communication. Their signal comprises a species-specific on/off light pattern repeated periodically, used by individual fireflies to advertise themselves to potential mates. Detecting individuals becomes increasingly challenging at high densities of fireflies. In this talk, I will explore how fireflies approach this problem while using physics and information-theory concepts, e.g., energetic cost and compression (minimization of bits representing information) and detectability (high signal-to-noise-ratio). The first approach involves signal amplification via synchronization within swarms containing tens of thousands of individuals. Our recent quantitative measurements of the three-dimensional spatiotemporal flashing pattern of synchronous firefly swarms allow us to validate a set of mathematical models that account for short-range spatial correlations and the signal's emergent periodicity. The second approach involves the evolutionary design of light patterns with increased detectability at other individuals' expense. Using a set of computational models, connected with experimental data, we observe an emergent periodicity in the resulting optimal sequences and demonstrate a method of reconstructing potential cost functions from the phylogenetic relationships of extant species alongside their characteristic flash patterns.