In this paper, wave regimes of rivulet flow and the formation of rivulet-like structures in isothermal and non-isothermal falling liquid film are investigated theoretically and experimentally. The Kapitsa-Shkadov approach is used for the theoretical description of the wave rivulet flow. A semi-analytical model has been developed for studying nonlinear waves in a single rectilinear rivulet. The equations of the model are derived by the method of weighted residuals by projecting the equations of the three-dimensional flow of a thin liquid layer onto a specially constructed system of 2N basic orthogonal polynomials. The stability of the rivulet flow is analyzed, and dispersion dependences for linear waves are obtained. Nonlinear wave modes of the rivulet flow are investigated numerically both for a rivulet, flowing on a vertical plate and a rivulet flowing down the lower surface of an inclined cylinder. The research is carried out within the framework of two differently posed problems, namely, the problem of stationary traveling waves with a given wavelength and the problem of spatial development of excited waves with a given frequency. The characteristics of nonlinear quasi-two-dimensional stationary traveling waves are obtained, as well as the spatial development of excited waves is studied. Comparison of the calculation results with the available experimental data has shown that the model used adequately describes in general the wave surface shape of the rivulet. For the theoretical description of the dynamics of a non-isothermal falling film, the IBL model equations are applied, modified taking into account the thermocapillary effect. A linear analysis of the stability of the heated film with respect to disturbances in the direction transverse to the flow is carried out, and a spatial growth increment of these disturbances downstream the flow is obtained. The results of numerical simulation have shown that a small transverse perturbation with a given wavelength evolves into a three-dimensional rivulet-like structure. It is shown that in experiments, the period of the rivulet structure corresponds to disturbances of maximum growth. The formation of a three-dimensional stationary rivulet-like structure in a locally heated film is simulated numerically for two types of heating conditions implemented in experiments: at a given constant wall temperature and at a given constant heat flux at the wall. The calculation results are in good concordance with the available experimental data.