A beginner to fly fishing may believe that the sport is mainly for catching trout and salmon. To some extent, this is true, at least in the sense that these fish are the most popular prey for anglers.
But the method one uses for catching trout and salmon can also be used for a whole variety of species. You can fly fish for pike, bass, panfish, grayling and carp, as well as marine species, such as redfish, snook, tarpon, bonefish and striped bass. Many fly anglers inadvertently catch other species, too. While going after their main target of trout, fishermen may also inadvertently catch other species too. These will include such things as chub, bream and rudd. But a growing number of anglers will consciously try to catch as many different species as possible with the fly.
Advances in fly fishing technology, and the development of stronger rods and reels, makes it possible these days to goo after larger predatory saltwater species. Depending on where you are in the world, the species that may be accessible include wahoo, tuna, marlin and even sharks.
To summarise, you can realistically target any species when fly fishing, and capture it on the fly, provided their main food source is replicated by the fly you are using, as well as the appropriate gear.