  Michael Boardman has been a major contributor to the theory of infinite loop
spaces and higher homotopy algebra. Indeed Boardman was the first to refer to
`homotopy everything'. One particular contribution which has had major progeny
is his use of `geometric' trees, combinatorial tress with lengths attached to
edges. Here is a modified version of the talk given to honor Mike on the
occassion of his 60th birthday. It is an idiosyncratic survey of parts of
homotopy algebra from Poincar\'e to the present day, with emphasis on
Boardman's original ideas, starting with his cubical subdivision of the
associahedra through recent applications in mathematical physics via
compactifications of moduli spaces.
