This talk explores emerging connections between sensing, modulation and coding through the unifying lens of sparse antenna array geometries. We first show that the canonical sensing problem of direction-of-arrival estimation can be naturally re-formulated as a so-called analog subspace coding problem. Subspace coding conventionally arises in non-coherent communications, where neither transmitter nor receiver knows the channel, and information is encoded in subspaces rather than vectors. This connection fosters new research problems at the intersection of coding theory and signal processing, inspiring both new structured subspace codes with near-optimal probability of error and noise-robust sparse arrays achieving high angular resolution. We also explore the versatile uses of antenna subset selection in integrated communications and sensing (ISAC), demonstrating that judicious antenna selection can offer enhanced sensing performance, as well as a balance between spectral and energy efficiency by making clever use of multiple antennas per radio-frequency (RF) chain. In both cases, we show how sparse array geometries are key to achieving high performance, reducing hardware complexity, and increasing energy efficiency of next-generation (NextG) multiple-input multiple-output (MIMO) systems equipped with far fewer RF chains than antennas.