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A brief overview of the QCD phase diagram at nonzero temperature and densityis provided. It is explained why standard lattice QCD techniques are notimmediately applicable for its determination, due to the sign problem. We thendiscuss a selection of recent lattice approaches that attempt to evade the signproblem and classify them according to the underlying principle: constrainedsimulations (density of states, histograms), holomorphicity (complex Langevin,Lefschetz thimbles), partial summations (clusters, subsets, bags) and change inintegration order (strong coupling, dual formulations).

Developments in lattice QCD for matter at high temperature and density