  Spin-orbit coupling (SOC) relates to the interaction between an electron's
motion and its spin, and is ubiquitous in solid-state systems. Although the
effect of SOC in normal-state phenomena has been extensively studied, its role
in superconducting hybrid structures and devices opens many unexplored
questions. In conjunction with broken symmetries and material inhomogeneities
within superconducting hybrid structures, SOC may have additional
contributions, beyond its effects in homogenous materials. Remarkably, even
with well-established magnetic or nonmagnetic materials and conventional s-wave
spin-singlet superconductors, SOC leads to emergent phenomena including
equal-spin triplet pairing and topological superconductivity (hosting Majorana
states), a modified current-phase relationship in Josephson junctions, and
nonreciprocal transport. SOC is also responsible for transforming
quasiparticles in superconducting structures which enhances the spin Hall
effect and changes spin dynamics. Taken together, SOC in superconducting hybrid
structures and the potential for electric tuning of the SOC strength, creates
fascinating possibilities to advance superconducting spintronic devices for
energy-efficient computing, and enable topological fault-tolerant quantum
computing. By providing a description of experimental techniques and
theoretical methods to study SOC, this Colloquium describes the current
understanding of resulting phenomena in superconducting structures and offers a
framework to select and design a growing class of materials systems where SOC
plays an important role.
