Abstract: A central role in the study of manifolds and their automorphisms is played by the homotopy type of the topological group Top(d) of homeomorphisms of d-dimensional Euclidean space, which is known to be closely related to algebraic K- and L-theory and, as discovered more recently, to operad theory and the study of graph complexes à la Kontsevich. The various pieces of information about Top(d) that are currently known can be packaged in terms of Weiss? orthogonal calculus, which is a general machinery to study functors on the category of real inner product spaces. This perspective does not only neatly clarify all that is known about Top(d) so far, but it also suggests a number of tempting tasks one could set oneself for the future study of Top(d). My plan for this talk is to give a gentle introduction to orthogonal calculus with a view towards Top(d), followed by explaining aspects of recent joint work with O. Randal-Williams.