I will review a new mechanism of the weak ergodicity breaking relevant for the experimentally realized Rydberg-atom quantum simulator. 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. In the single-particle case, quantum scars correspond to wave functions concentrated in the vicinity of unstable periodic classical trajectories. I will demonstrate that many-body scars appear in the Fibonacci chain, a model with a constrained local Hilbert space which can be realized by a Rydberg chain. I will focus on the relation between scars and time dependent variational principle over matrix product states and will discuss the relation between quantum scars and quantum many-body control problems.