  We survey recent developments in the study of probabilistic complexity
classes. While the evidence seems to support the conjecture that probabilism
can be deterministically simulated with relatively low overhead, i.e., that
$P=BPP$, it also indicates that this may be a difficult question to resolve. In
fact, proving that probabilistic algorithms have non-trivial deterministic
simulations is basically equivalent to proving circuit lower bounds, either in
the algebraic or Boolean models.
