A personal account is presented for the present status of mathematical chemistry, with emphasis on non-numerical applications. These use mainly graph-theoretical concepts. Most computational chemical applications involve quantum chemistry and are therefore largely reducible to physics, while discrete mathematical applications often do not. A survey is provided for opinions and definitions of mathematical chemistry, and then for journals, books and book series, as well as symposia of mathematical chemistry. ''... In jeder einzelnen Naturlehre gibt es nur so viel exakte Wissenschaft, wie sie Mathematik entha¨lt -so kann Chemie nichts mehr als Kunst oder ExFoundations of Chemistry (2005) 7: 289-306 Ó Springer 2005