Recent progress in lattice QCD at finite density

We review recent progress in lattice QCD at finite density. The phase diagram of QCD and the equation of state at finite temperature and density are discussed. In particular, we focus on the critical point terminating a first order phase transition line in the high density region. The critical point is one of the most interesting features that may be discovered in heavy-ion collision experiments. We summarize the current discussion on the existence of a critical point in the QCD phase diagram and discuss some attempts to find the critical point by numerical simulations.