I will review a new mechanism of the weak ergodicity breaking from quantum many-body scars. 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. I will demonstrate that quantum many-body scars appear in the PXP model with a constrained local Hilbert space which can be realized by a Rydberg chain. Next, I will discuss the relation between scars and time dependent variational principle over matrix product states (TDVP). I will formulate the solution to the optimal control problem that relies on TDVP language and demonstrate that this approach allows to construct nontrivial Floquet models with quantum many-body scars. Finally, I will demonstrate the anomalous energy transport in the PXP model with quantum scars, and will discuss the potential relation between quantum scars, TDVP trajectories, and transport.