There is to date no overarching classification theorem for C*-algebras, which means the theory of C*-algebras is an example-driven field of mathematics. Perhaps the most important class of examples are group C*-algebras, which are as old as the field itself. An analogous construction of C*-algebras associated to semigroups has been an active area of research among operator algebraists since Coburn’s Theorem regarding the universality of the C*-algebra generated a single isometry appeared in the 1960s. In July this year, Newcastle will host the AMSI/AustMS sponsored event "Interactions between operator algebras and semigroups". In this talk I will give a gentle introduction to the theory of semigroup C*-algebras and perhaps it will convince some of you to come along and take part in the meeting.