Summary: Material media containing dense distributions of linear, string-like objects are considered. Dislocation lines in structured solids and supercurrent vortices in type-II superconductors are exemplifications of such objects. The strings are assumed to carry a quantized Abelian topological charge, such as the Burgers vector or magnetic flux. The basic formulations of statistical physics of such systems are discussed. Contrary to the special cases of rectilinear strings, which reduce effectively to 2D systems of point-like particles, the statistical physics of 3D networks of flexible strings is treated on a stand alone basis from the first principles. The presented description takes into account the quenched, thermal, and quantum disorder in a unified way. Implications for the macroscopic setting are discussed.