The richness of phenomena occurring in heavy-ion collisions calls for microscopic approaches where the motion of each nucleon is treated quantum mechanically. The most popular microscopic approach for low-energy collisions between atomic nuclei is the time-dependent Hartree-Fock (TDHF) theory, providing a mean-field dynamics of the system. The TDHF approach and some of its extensions are used to predict the evolution of out-of-equilibrium nuclear systems. The formation of di-nuclear systems with a structure close to molecular states is investigated. In particular, lifetimes and exit channels are described. The formation of light molecules and the dynamics of α-clustering are discussed. Di-nuclear systems formed in transfer, deep-inelastic, and quasi-fission reactions, as well as hyperheavy molecules produced in reactions between actinides are also investigated. The formation and stability of structures in neutron star crusts are finally discussed.