Recent advances in thermodiffusion (Soret effect) in binary and higher multicomponent liquid mixtures are reviewed. The mixtures studied include the hydrocarbon, associating, molten metal and semiconductor, polymer, and DNA mixtures.  The emphasis is placed on the theoretical works, particularly models based on the nonequilibrium thermodynamics, although other approaches such as the statistical-kinetic and hydrodynamics approaches are discussed as well. For each mixture, the major theoretical and experimental works are discussed and the research trends and challenges are addressed. Some of the challenges include a need for combining various methods to develop a comprehensive theoretical model or at least to try to understand the differences and pros and cons of each approach. Thermodiffusion and ordinary diffusion coefficients are scarce in some mixtures such as binary DNA, molten metal and metal-semiconductor mixtures and all ternary mixtures.  Undressing of the molecular structure of associating mixtures, and modeling of thermodiffusion in such mixtures are also very challenging.