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In recent years there has been much progress on the investigation of the QCDphase diagram with lattice QCD simulations. In this review I focus on thedevelopments in the last two years. Especially the addition of externalinfluences or new parameter ranges yield an increasing number of interestingresults. I discuss the progress for small, finite densities from bothanalytical continuation and Complex Langevin simulations, for heavy quark boundstates (quarkonium), the dependence on the quark masses (Columbia plot) and theinfluence of a magnetic field. Many of these conditions are relevant for theunderstanding of both the QCD transition in the early universe and heavy ioncollision experiments which are conducted for example at the LHC and RHIC.

Overview of the QCD phase diagram -- Recent progress from the lattice