Survey on the Asymptotic Dirichlet Problem for the Minimal Surface Equation

We give a survey on the development of study asymptotic Dirichlet problem for minimal surface equation Cartan-Hadamard manifolds. Part this is based introductory part doctoral dissertation author. The paper organised as follows. First we introduce manifolds and concept problem, then discuss about results describe methods used in proofs. In end mention some nonsolvability problem.