I will present the K-theoretic formulation of the bulk-boundary principle and exemplify how the machinery works for several classes of aperiodic systems, ranging from quasi-periodic to quasi-crystals and Moire patterns. For this, I will construct the hull and the algebras of observables, pinpointing similarities but also fine differences between various systems, which can be rigorously spotted using K-theory. Predictions and numerical confirmations will be provided.