This Thesis is devoted to the study of particle mobility in polar lattice gases, thatis, systems of particles with a large magnetic or electric dipole moment loaded in a deep optical lattice, which may move between sites via hopping. Our detailed analysis of different scenarios shows that inter-site dipole-dipole interactions largely handicap particle motion, resulting in a lattice dynamics that differs qualitatively, and not only quantitatively, to that expected both for non-dipolar gases, and for systems with exclusively nearest-neighbor interactions. We first discuss how the formation of dynamically-bound nearest-neighbor dimers for large enough dipolar interactions, results in an anomalously slow dynamics and quasi-localization due to the formation of dimer clusters. Moreover, we show that even modest inter-site interactions result in the formation of self-bound lattice droplets. We then extend the discussion to general states, placing the discussion in the frame of current studies on disorder-free localization, dynamical constraints and Hilbert-space fragmentation. We are particularly concerned with the difference between a polar lattice gas and a system with purely nearest-neighbor interactions. In the latter, strong-enough inter-site interactions lead to fragmentation, but resonant dynamics remains possible within a fragment, precluding disorder-free spatial localization. In contrast, in a polar gas, the presence of the dipolar tail shatters the Hilbert space, and in addition disrupts the resonant mechanism characteristic of the nearest-neighbor model. As a result, we show that the particle dynamics is dramatically slowed-down, and eventually localized in absence of any disorder, for interaction strengths within reach of experiments. Furthermore, although most of the results of this Thesis concern one-dimensional systems, most of the results can be extrapolated to higher dimensions. Moreover, we show that the dynamics in two-dimensional polar lattice gases presents peculiar features, due to the fact that dynamically-bound dimers experience a lattice different than that of individual particles. In particular, dimers in triangular lattices move in an effective kagome lattice, presenting an effective flat band. We show that the presence of flat-band dimers results in a peculiar multi-scaled quantum walk dynamics, and in a long-lived memory of initial conditions in absence of any disorder. The results in this Thesis open exciting perspectives in what concerns particle dynamics and disorder-free localization in on-going and future experiments with magnetic atoms and polar molecules in optical lattices. Furthermore, our findings may be easily extrapolated to other power-law interactions, as those realizable using trapped ions.