Abstract: Some fundamental concepts and problems in the research field of the structural topology optimization are introduced briefly. The essential characteristics of the truss-like and its discretization are analyzed. The classical analytical solutions as the benchmarks are listed in the references. The optimization strategies and the characteristics of various numerical methods for the structural topology optimization are reviewed. The numerical instabilities, such as the mesh-dependencies, the singular optima, the checkerboards and the local constraints, commonly in the structural topology optimization, are explained. The fundamental principles of the optimality criteria, the sequential programming and the heuristic methods are discussed.