Recent experiments on large chains of Rydberg atoms have found surprising signatures of non-ergodic dynamics, such as robust periodic revivals in global quenches from certain initial states. This weak form of ergodicity breaking has been dubbed "quantum many-body scars" by analogy with unstable classical periodic orbits of a single particle confined to a stadium billiard. In this talk, I will argue that this analogy can be further strengthened by formulating a mean-field type approximation for the atoms residing on even and odd sublattices of the chain.This approach not only provides accurate approximations of scarred eigenstates of this non-integrable system, but it also has a direct relation with the system's semiclassical dynamics. In the second part of the talk, I will present a proposal for the experimental realisation of quantum many-body scars using a 1D Fermi-Hubbard model in a tilted optical lattice. This platform allows to probe the interplay of scars with other forms of ergodicity breaking, such as Stark many-body localisation and Hilbert space fragmentation due to a dipole moment symmetry.