I will describe a variety of applications of non-invertible symmetries and dualities. One use is to extend Kramers-Wannier duality to a large class of models, explaining exact degeneracies between non-(conventional) symmetry-related ground states as well as in the low-energy spectrum. For critical models, the universal behaviour under Dehn twists gives exact results for scaling dimensions, while gluing a topological defect to a boundary allows universal ratios of the boundary g-factor to be computed exactly on the lattice. Time permitting I will also describe analogous 2+1d models that provide good candidates for realising chiral topological order on the lattice.