Abstract: “The usual methods for studying Waring’s problem (i.e. finding how many $s$-th powers does one need to represent all the integers?) require a rather large number of summands. ErdundefinedH{o}s and Rundefined’{e}nyi introduced in 1960 a probability model for studying sums of $s$ numbers which are $s$-th powers. Their model has been largely developed since then. After introducing the subject, the talk will focus on this probabilistic approach, up to the most recent contributions obtained jointly with the late Javier Cilleruelo. This is a colloquium talk where no specialised knowledge of number theory nor probability theory is required.”