FPGAs run the execution of strategy, everything else is done by high level software/systems. FPGAs are connected directly to the exchange and also help receive a feed of market data (in addition to other market data feeds).
I guess that depends on how close to the exchange you want to be. If your strategies were extremely latency sensitive, you might want to have not just the execution logic, but the larger algo framework on there too. This is particularly true of strategies that make use of order book dynamics.
A big advantage that FPGAs have is that they are fast at "single threaded" tasks so they can parse data in formats that aren't easy to parse quickly, like the XML-based FIX protocol.
I'm not sure FPGAs are 'suited' for parsing formats with lots of variable lengths and data dependencies like XML, but obviously they can be faster than typical Von Neumann. I know binary market data streams were one of the first uses in the financial industry.
