  We prove the existence of Bridgeland stability conditions on the Kuznetsov
components of Gushel-Mukai varieties, and describe the structure of moduli
spaces of Bridgeland semistable objects in these categories in the
even-dimensional case. As applications, we construct a new infinite series of
unirational locally complete families of polarized hyperk\"{a}hler varieties of
K3 type, and characterize Hodge-theoretically when the Kuznetsov component of
an even-dimensional Gushel-Mukai variety is equivalent to the derived category
of a K3 surface.
