Topological quantum matter typically arises in gapped (massive) systems, where topological invariants and their associated quantized experimental signatures are protected by the energy gap separating ground- and excited- state(s). Understanding topological properties of such gapped systems has led to tremendous progress in theoretically classifying and characterizing gapped phases of matter, even in the presence of strong correlations. By comparison, gapless phases such as strange-metals, non-Fermi liquids, spin-liquids, and spin-ices, are relatively poorly understood despite their strong experimental relevance. Traditionally, one might not expect such complex gapless phases to yield similar non-perturbative insights tied to sharply quantized topological invariants. Notable counterexamples to this expectation are gapless surface states of higher-dimensional topological phases, which inherent quantized anomalous properties associated with the bulk topology. In this talk, I will describe new contexts in which effectively anomalous gapless systems can effectively arise without a higher-dimensional topological bulk, but whose physical properties are nonetheless strongly constrained by sharply quantized anomalies. I will first recount recent experimental observations of magneto-transport signatures of topological and anomalous features in 3d topological semimetals. I will then describe how unconventional symmetries can lead to non-perturbative theoretical insights into strongly correlated insights based on crystalline symmetries, and dualities, which could shed light on complex systems such as partially filled Landau levels in graphene and frustrated magnetic materials with disorder.