**Abstract :** In certain problems in a variety of applied
probability settings (from probabilistic analysis of algorithms to
statistical physics), the central requirement is to solve a recursive
distributional equation of the form $X =^d g((\xi_i,X_i),i\geq
1)$. Here $(\xi_i)$ and $g(\cdot)$ are given and the $X_i$ are
independent copies of the unknown distribution X. We survey this
area, emphasizing examples where the function $g(\cdot)$ is
essentially a ``maximum'' or ``minimum'' function. We draw attention
to the theoretical question of endogeny: in the associated recursive
tree process $X_i$, are the $X_i$ measurable functions of the
innovations process $(\xi_i)$ ?

[Joint work with David J. Aldous]