While the BPS state counting problem in general toric Calabi-Yau manifolds was solved a decade ago, it has long remained an unsolved problem to identify the underlying BPS state algebra. Recently, we solved this problem by introducing a new infinite-dimensional algebra, the BPS quiver Yangian. We constructed representations of the algebra in terms of crystal melting,and derived the representations physically from supersymmetric quantum mechanics. This talk is based on two papers arXiv:2003.08909 and arXiv:2008.07006, in collaboration with Wei Li and Dmitry Galakhov.