What gets blown when you hook up jumper cables backwards

Could be all sorts of things which are hard to predict. I would start by checking all the fuses including the fuseable link.

Good question. How dead was your battery? Did you actually try and start your vehicle? What happened to the other vehicle? Did it die as well? It should have. Suggest you get an ODB II tester and see if the computer will respond. If not, the ECM/PCM is toast for starters. If the lights were on, they are now bad. Some of the sensors may have survived because they are direct connected the computer. Fuses, fusible links, starter relay, starter solenoid, voltage regulator in the alternator are most likely toast.