  This thesis contains a collection of algorithms for working with the twisted
groups of Lie type known as Suzuki groups, and small and large Ree groups. The
two main problems under consideration are constructive recognition and
constructive membership testing. We also consider problems of generating and
conjugating Sylow and maximal subgroups. The algorithms are motivated by, and
form a part of, the Matrix Group Recognition Project. Obtaining both
theoretically and practically efficient algorithms has been a central goal. The
algorithms have been developed with, and implemented in, the computer algebra
system MAGMA.
