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One of the appealing aspects of condensed matter physics is the emergence of new collective behavior and quasiparticle excitations as a consequence of interactions between particles. This talk begins with one-dimensional materials, which have long been known to support unusual metallic states in which the electron spin and charge separate and travel with different velocities. However, the collective physics of even simple systems, including the paradigmatic Heisenberg spin chain, only became clear in the last few years: even at room temperature, the spins form an unusual quantum fluid related to the Kardar-Parisi-Zhang universality class familiar from soft condensed matter physics. This prediction leads to consequences for neutron scattering experiments under reasonable conditions, which were recently observed by a study of KCuF3 (Scheie et al., Nat. Phys., 2021). A different kind of breakup or fractionalization of the electron can happen in higher dimensions; it has been difficult to find in quantum magnets, but new insight is coming from concepts and methods originating in quantum information theory. The last part of the talk discusses the renaissance of interest in interacting spins on a triangular lattice, following on the original spin liquid idea introduced by Anderson in 1973. An increasing body of evidence from theory and experiment suggests the appearance of exotic states with an energy gap in triangular lattice compounds near a Mott transition. Talk presented at the ICAM Global Summit 2022 January 14, 2022