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We will discuss the dynamics of classical and quantum many-body systems in the presence of constraints. This is understood in a really broad sense of the term, ranging from lattice gauge theories, over fractonic systems to general spatially-modulated symmetries. We will first show that the combination of charge and dipole conservation leads to an extensive fragmentation of the Hilbert space, which, in turn, can lead to a breakdown of thermalization. As a concrete example, we will investigate the out-of-equilibrium dynamics of one-dimensional spin-1 models that conserve charge (total Sz) and its associated dipole moment, and show that for any finite range of interactions, the system exhibits nonthermal eigenstates appearing throughout the entire spectrum. In particular, we will find that the infinite temperature autocorrelation saturates to a finite value, which we will attribute to the strong fragmentation of the Hilbert space into exponentially many invariant subspaces. More generally, we will classify these systems as weakly or strongly fragmented, and obtain additional dynamical features for each scenario, as for example subdifussion in the former case. We will then find that such systems naturally arise as effective descriptions of interacting systems in the presence of a strong tilted field, and briefly discuss recent experimental results. At this point, it might become clear that such “unusual’’ symmetries lead to rather rich dynamical behavior. To conclude my talk, we will extend these symmetries to more general “spatially modulated’’ ones, uncovering two new instances with (quasi)-periodic and exponential modulations. If time permits, I will briefly mention some previous work in which we used a non-Gaussian ansatz to address lattice gauge theories in 1D.