  Associated to a Mukai flop X ---> X' is on the one hand a sequence of
equivalences D(X) -> D(X'), due to Kawamata and Namikawa, and on the other hand
a sequence of autoequivalences of D(X), due to Huybrechts and Thomas. We work
out a complete picture of the relationship between the two. We do the same for
standard flops, relating Bondal and Orlov's derived equivalences to spherical
twists, extending a well-known story for the Atiyah flop to higher dimensions.
