I will present recent results on light nuclei production in relativistic heavy-ion collisions within two extensions of the thermal model approach. First, a canonical formulation of the statistical model will be exploited to analyze the suppression of light nuclei abundances in small systems created in pp and pA collisions at the LHC. Second, the evolution of light nuclei yields during the long-lived hadronic phase in central collisions of heavy ions is described using the cosmological Saha equation approach, providing clues to the remarkable success of thermal models in describing the production of loosely bound states. Finally, I will discuss the feeddown contributions from excited nuclear states, which are found to be sizable at energies corresponding to the RHIC beam energy scan.