The concept of ultraproducts in the context of tracial von Neumann algebras was effectively introduced by Wright in 1954. Since then, it has been used as a central technique in several important works on the classification and structure theory of von Neumann algebras, including works of McDuff and Connes. Developments beginning in the 2010s also connected the concept to ultraproducts in model theory. In this talk, I will be presenting a general overview of the technique and relevant results, both from a von Neumann algebra and from a continuous model theory perspective. I will also present several of my works, with various collaborators, that apply the technique and related techniques in C*-algebras and group theory.