In this talk, I will present an overview over recent developments on superconductivity with Cooper pairs that exhibit a non-zero total spin. Superconducting order with nonzero spin can be realized in unconventional, spin-triplet, superconductors. Alternatively, it can be induced from conventional superconducting pair condensates when brought in contact with a magnetic material in a proximity structure. With the beginning of the new millennium, a series of pivotal predictions and experimental discoveries relating to the interplay between superconductivity and magnetism in heterostructures have been made. Non-collinear magnetism leads to odd-frequency triplet pairing, with equal-spin Cooper pairs as carriers for non-dissipative spin transport. Geometric Berry phases appear in structures with non-coplanar magnetization profile, enhancing functionality. Spin-orbit locking may lead to topological superconductivity. I also discuss recent experiments on enhanced spin-pumping in a non-local ferromagnet-superconductor structure and discuss implications for theory.