This paper presents a review of analytical methods in seepage theory of civil engineering, hydrogeology and irrigation engineering. According to the authors, these methods are necessary not only to develop and test numerical algorithms, but also to gain a deeper understanding of the underlying physics, as well as for the parametric analysis of complex flow patterns and the optimization of the seepage field properties. In particular, under consideration are methods of inverse boundary value problems, variational-topological methods (M. A. Lavrent'ev, G. N. Polozhij) and optimization methods.