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Galaxy spins are shaped by multiple physical processes operating across cosmic time. In the early universe, galaxies acquire angular momentum through tidal torques from the surrounding large-scale structures. At later times, the non-linear growth of the universe produces vorticity fields, while galaxy interactions along the cosmic web drive spin reorientations. In this talk, I present findings from the IllustrisTNG cosmological simulations on three major aspects of galaxy spin evolution. First, I examine the spin-orbit alignment in galaxy pairs, showing how galaxy-galaxy interactions lead to changes in spin directions. Second, I discuss the intrinsic spin alignment with the cosmic web, focusing on the peculiar behavior of inner stellar spins compared to dark matter halos. Third, I address the role of initial conditions by quantifying the primordial misalignment between the inertia and tidal tensors, revealing its connection to present-day galaxy properties.