  This expository paper advocates an approach to physics in which ``typicality"
is identified with a suitable form of algorithmic randomness. To this end
various theorems from mathematics and physics are reviewed. Their original
versions state that some property F(x) holds for P-almost all x in X, where P
is a probability measure on some space X. Their more refined (and typically
more recent) formulations show that F(x) holds for all P-random x in X. The
computational notion of P-randomness used here generalizes the one introduced
by Martin-L"of in 1966 in a way now standard in algorithmic randomness.
Examples come from probability theory, analysis, dynamical systems/ergodic
theory, statistical mechanics, and quantum mechanics (especially hidden
variable theories). An underlying philosophical theme, inherited from von Mises
and Kolmogorov, is the interplay between probability and randomness,
especially: which comes first?
