  The past two decades have seen an explosion of work on Josephson junctions
containing ferromagnetic materials. Such junctions are under consideration for
applications in digital superconducting logic and memory. In the presence of
the exchange field, spin-singlet Cooper pairs from conventional superconductors
undergo rapid oscillations in phase as they propagate through a ferromagnetic
material. As a result, the ground-state phase difference across a ferromagnetic
Josephson junction oscillates between 0 and $\pi$ as a function of the
thickness of the ferromagnetic material. $\pi$-junctions have been proposed as
circuit elements in superconducting digital logic and in certain qubit designs
for quantum computing. If a junction contains two or more ferromagnetic layers
whose relative magnetization directions can be controlled by a small applied
magnetic field, then the junction can serve as the foundation for a memory
cell. Success in all of those applications requires careful choices of
ferromagnetic materials. Often, materials that optimize magnetic properties do
not optimize supercurrent propagation, and vice versa. In this review we
discuss the significant progress that has been made in identifying and testing
a wide range of ferromagnetic materials in Josephson junctions over the past
two decades. The review concentrates on ferromagnetic metals, partly because
eventual industrial applications of ferromagnetic Josephson junctions will most
likely start with metallic ferromagnets (either in all metal junctions or
junctions containing also an insulating layer). We will briefly mention work on
non-metallic barriers, including ferromagnetic insulators, and some of the
exciting work on spin-triplet supercurrent in junctions containing noncollinear
magnetic inhomogeneity.
