Results on open charm and beauty production and on the search for top
production in high-energy electron-proton collisions at HERA are reviewed. This
includes a discussion of relevant theoretical aspects, a summary of the
available measurements and measurement techniques, and their impact on improved
understanding of QCD and its parameters, such as parton density functions and
charm- and beauty-quark masses. The impact of these results on measurements at
the LHC and elsewhere is also addressed.Comment: 103 pages, 60 figures, to be published in Prog. Part. Nucl. Phy