We review some recent results on the development of efficient tree tensor network algorithms and their applications to high-dimensional many-body quantum systems and machine learning problems. In particular, we present results on topological two-dimensional systems, two dimensional Rydberg atom systems, and two and three-dimensional lattice gauge theories at zero and finite density. Finally, we present their application to LHCb events classification and to the study of open many-body quantum systems, specifically to the computation of the entanglement of formation in critical many-body quantum systems at finite temperature, resulting in the generalization of the Calabrese-Cardy formula to open systems.