  We provide a simple formula that accurately approximates the first crossing
distribution of barriers having a wide variety of shapes, by random walks with
a wide range of correlations between steps. Special cases of it are useful for
estimating halo abundances, evolution, and bias, as well as the nonlinear
counts in cells distribution. We discuss how it can be extended to allow for
the dependence of the barrier on quantities other than overdensity, to
construct an excursion set model for peaks, and to show why assembly and scale
dependent bias are generic even at the linear level.
