The C∗ -correspondences are generalised morphism of C∗ algebras. We shall discuss the benefits of studying the bicategory of C∗ -algebras obtained using these morphisms. We shall see the topological analogue of C ∗ -correspondences; this work is a part of the “Algebra-Topology (or Geometry) Dictionary” type of projects in Analysis whose origin can be traced back to the well-known theorem of Gelfand and Naimark. We shall discuss our recent work on proper topological correspondences. Along the way, the theory of groupoid C∗ -algebras, locally free actions of groupoids and other necessary notions shall be discussed. This is a seminar talk with a slight flavour of a colloquium talk.