From lattice to observables: Real and virtual experiments for exploring hot and dense QCD

Relativistic heavy-ion collisions and the lattice QCD Monte-Carlo simulations are important ``experimental’’ tools for investigating the properties of the medium described by QCD under extreme conditions. After briefly examining their characteristics, I pick up the study of the critical points in QCD as an example of the research subjects that these two tools play complementary roles and discuss recent topics that have been achieved with the use of each tool.