Quantum many-body scar states represent a recent discovery that challenges the paradigm of eigenstate thermalization hypothesis (ETH). They came to the fore as a very visual scarring of the many-body spectrum in a so-called PXP model used to describe a Harvard 51-atom quantum simulator experiment that found unusual thermalization from a state at effective infinite temperature. I will describe our finding that the PXP model has exact ETH-violating eigenstates that persist in the thermodynamic limit and how we can approximate other observed scar states in the model. I will also discuss the fate of the exact scar states under perturbations and will show evidence that they eventually thermalize but with parametrically long thermalization time and can have observable experimental consequences.