Although I will explain the basics of the underlying model theory - continuous logic and metric structures, I would like to examine a number of active directions of the interaction between model theory and operator algebras. These include a look a model theoretic formulation of the Connes embedding problem and some its consequences, the role of model theoretic stability, and classes of operator algebras and omitting types. This is joint work variously with Ilijas Farah, David Sherman, Isaac Goldbring, Thomas Sinclair and a Fields-MITACS undergraduate research team.