Polarized neutron reflectivity and scattering has established itself as one of the most important experimental methods for the analysis of magnetic nanostructures and spintronic materials. With this method, seminal contributions have been made to the physics of thin magnetic films, interfaces, and superlattices, including collinear and noncollinear exchange coupling. Another rich area is the exchange coupling phenomena between ferromagnetic and antiferromagnetic layers. Presently neutron scattering from laterally patterned magnetic arrays has become very active for the understanding of domain structures, domain reversals, and correlation effects. Established more than 25 years ago, polarized neutron reflectivity was focused mainly on the specularly reflected intensity. With the advent of area detectors and efficient wide‐angle spin analyzers, the off‐specular diffuse scattering could be analyzed, contributing to a more complete picture of the physics of magnetic nanostructures and patterned arrays. In this review a basic introduction into the fundamentals of polarized neutron reflectivity is provided, including specular and off‐specular scattering. For the description of the off‐specular part, the distorted wave Born approximation has rigorously been applied and features missed in the simpler Born approximation are pointed out. The methods are illustrated by a number of examples from research into magnetic thin films, spin valves, magnetic multilayers, exchange bias systems, spintronic materials, and periodic magnetic arrays of islands and stripes.