This overview introduces hypercomplex algebras and hypercomplex analysis, mapping out the historical developments and the major domains of research and application. It allows to see how the various contributions collected in this proceedings volume are related and advance both research and applications. It begins with some historical remarks on early developments in hypercomplex algebra and analysis in the nineteenth and twentieth centuries, an overview of hypercomplex algebras with the definition of Clifford geometric algebras, and examples of their formulation and basic properties in two and three Euclidean dimensions. Next is a brief treatment of projective geometric algebra, of spacetime algebra of four-dimensional Minkowski space, of conformal geometric algebra, and of hypercomplex algebras which are non-associative, like the octonions and the Okubo algebra. Then spinor algebra and related topics are treated as well as the development of hypercomplex analysis, based on Clifford algebra, quaternions, octonions, and encompassing discrete function theories. Applications in physics range from Grassmann’s theory of tides to the Standard Model of elementary particle physics. Finally, technological applications of the last 30–40 years including modern applications to advanced neural networks and PDE modeling are reviewed, as well as various other applications published in recent years