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.
