Discovered in 1962, the divalent ferromagnetic semiconductor EuS (T-C = 16.5 K, E-g = 1.65 eV) has remained constantly relevant to the engineering of novel magnetically active interfaces, heterostructures, and multilayer sequences and to combination with topological materials. Because detailed information on the electronic structure of EuS and, in particular, its evolution across T-C is not well-represented in the literature but is essential for the development of new functional systems, the present work aims at filling this gap. Our angle-resolved photoemission measurements complemented with first-principles calculations demonstrate how the electronic structure of EuS evolves across a paramagnetic-ferromagnetic transition. Our results emphasize the importance of the strong Eu 4f-S 3p mixing for exchange-magnetic splittings of the sulfur-derived bands as well as coupling between f and d orbitals of neighboring Eu atoms to derive the value of T-C accurately. The 4f-3p mixing facilitates the coupling between 4f and 5d orbitals of neighboring Eu atoms, which mainly governs the exchange interaction in EuS.