  We survey facts mostly emerging from the seminal results of Alan Cobham
obtained in the late sixties and early seventies. We do not attempt to be
exhaustive but try instead to give some personal interpretations and some
research directions. We discuss the notion of numeration systems, recognizable
sets of integers and automatic sequences. We briefly sketch some results about
transcendence related to the representation of real numbers. We conclude with
some applications to combinatorial game theory and verification of
infinite-state systems and present a list of open problems.
