The notion that complexity increases in evolution is widely accepted,
but the best-known evidence is highly impressionistic. Here I propose
a scheme for understanding complexity that provides a conceptual basis
for objective measurement. The scheme also shows complexity to be a b
road term covering four independent types. For each type, I describe s
ome of the measures that have been devised and review the evidence for
trends in the maximum and mean. In metazoans as a whole, there is goo
d evidence only for an early Phanerozoic trend, and only in one type o
f complexity. For each of the other types, some trends have been docum
ented, but only in a small number of metazoan subgroups.