Structure optimizations are fundamental techniques in first-principles calculations. From the structure optimization, we can determine a wide range of things, such as lattice constants of crystals, the spacing between a surface atom layer and a subsurface layer, and the adsorption sites of adsorbates. This paper discusses the structure optimization methods and the relating methods. First, the paper discusses the requirement of highly accurate total energies and its effect on the treatment of the calculated total energies. Second, two common algorithms utilizing atomic forces for the structure optimization are introduced. Third, the error in the optimization is discussed. It can be classified into two groups. The first one comes from how the electronic correlation is treated. The second one comes from the numerical convergence of the calculation. Last, as advanced topics, methods for (free) energy barrier are briefly introduced.