As FPGAs can have many things working in parallel and may not contain an embedded processor at all then special tools are used for debugging. Most FPGA vendors have "embedded instruments" that can be added to your design and that provide visibility into the hardware.
Xilinx - Chipscope, now Vivado Labtools (requires paid license)
Altera - SignalTap (free)
Lattice - Reveal (free)
Microsemi - need to figure out
There are some attempts for platform neutral or cross platform embeded instruments, Altium is/has tried this and opencores OpenRisc seems to have something too.
Sump LA can of course also be used for internal debug..