The concept of geometrical frustration has led to rich insights into condensed matter physics, especially as a mechanism to produce exotic low-energy states of matter. Here we show that frustration provides a natural vehicle to generate models exhibiting anomalous thermalization of various types within high-energy states. We consider three classes of nonintegrable frustrated spin models: (I) systems with local conserved quantities where the number of symmetry sectors grows exponentially with the system size but more slowly than the Hilbert space dimension, (II) systems with exact eigenstates that are singlet coverings, and (III) flatband systems hosting magnon crystals. We argue that several one- and two-dimensional models from class I exhibit disorder-free localization in high-energy states so that information propagation is dynamically inhibited on length scales greater than a few lattice spacings. We further show that models of classes II and III exhibit quantum many-body scars: eigenstates of nonintegrable Hamiltonians with finite-energy density and anomalously low-entanglement entropy. Our results demonstrate that magnetic frustration supplies a means to systematically construct classes of nonintegrable models exhibiting anomalous thermalization in mid-spectrum states.