The statistical mechanics description of many-particle systems rests on the assumption of ergodicity, the ability of a system to explore all allowed configurations in the phase space. For quantum many-body systems statistical mechanics predicts the equilibration of highly excited non-equilibrium state towards a featureless thermal state. Hence, it is highly desirable to explore possible ways to avoid ergodicity in quantum systems. Many-body localization presents one generic mechanism for a strong violation of ergodicity relying on the presence of quenched disorder. In my talk I will discuss a different mechanism of the weak ergodicity breaking relevant for the experimentally realized Rydberg-atom quantum simulator [1]. This mechanism arises from the presence of special eigenstates in the many-body spectrum that are reminiscent of quantum scars in chaotic non-interacting systems [2]. I will construct the weak deformation of the Rydberg chain Hamiltonian that makes revivals virtually perfect [3]. In the second part of the talk I will provide a dynamical perspective on quantum scars. I will show the occurrence of mixed phase space within time-dependent variational principle (TDVP) description of dynamics. I will use TDVP to find new scars and explore their response to perturbations of the Hamiltonian. Finally, I will argue that the mixed phase space generally leads to non-universal dependence of thermalization on the initial state and discuss a new opportunities for the creation of novel states with long-lived coherence in systems that are now experimentally realizable [1].