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We review how lattice QCD can contribute to the prediction and the comprehension of tetraquarks, pentaquarks and related exotic hadrons, with at least one heavy quark. We include all families of exotic hadrons, except for the quarkless glueballs and the hexaquarks which are related to nuclear physics. Since the discovery of quarks and the development of the QCD theory, there has been a large interest in exotic hadrons, initiated by the tetraquark models developed by Jaffe in 1977. Lattice QCD, being a first principle approach to solve non-perturbative QCD, has been crucial not only to compute precise results, but also to inspire research in hadronic physics. In the new millennium, this interest exploded with several experimental discoveries of tetraquark and pentaquark resonances with heavy quarks, starting with the Zc and Zb. Lattice QCD has not yet been able to comprehend this Z class of tetraquarks, and is developing new methods to determine their masses, decay widths and decay processes. The interest in tetraquarks was also fuelled by the lattice QCD prediction of a second class of tetraquarks such as the Tbb, boundstates in the sense of having no strong decays. Recently, the Tcc tetraquark, first predicted with quark models in 1982 by Richard et al, was observed experimentally. We expect the lattice QCD community will be able to explore this T class of tetraquarks in more detail and with very precise results. We report on all the different direct and indirect approaches that lattice QCD, with more focus on tetraquarks, has been employing to study exotic hadrons with at least one heavy quark. We also briefly review the experimental progress in observing tetraquarks and pentaquarks, and some of the theoretical paradigms of tetraquarks, including three different types of mechanisms (diquark, molecular and s pole), comparing them with the results of lattice QCD.