The living fish group closest to tetrapods is lungfish.
Lungfish are lobe-finned fishes in the group Dipnoi, part of the same broad branch of vertebrate evolution that includes tetrapods. Genetic and anatomical evidence places living lungfish closer to amphibians, reptiles, birds, and mammals than coelacanths or any ray-finned fish.
Their relationship is especially interesting because lungfish retain several traits associated with the fish-to-tetrapod transition. They possess lungs and can breathe air, while their fleshy fins contain internal skeletal elements. Some species can survive drought by burrowing into mud and entering a dormant state. Their closest relationship to tetrapods does not mean lungfish are their direct ancestors; both groups descended from an older common ancestor roughly 420 million years ago.
A common mix-up is coelacanths, another famous lobe-finned fish. Coelacanths are evolutionary relatives of tetrapods, but molecular studies generally place them on a branch that split earlier than the lungfish-tetrapod lineage.