At the end of the 19th century Hurwitz formulated a problem on the existence of sums-of-squares identities. This problem remains widely open. It turns out that the question can be rephrased in various ways and arises in many different contexts, algebraic, geometric, topological ... Furthermore, Hurwitz's work on sums-of-squares is extensively used by engineers in information theory to construct certain codes for wireless communication. We will recall the problem of Hurwitz and discuss some of the related topics. We will describe a method to construct solutions to the problem explicitly. The method is based on nonassociative algebras generalizing the octonions.