See , basically electronics is a vast field. You need to decide whether you wanna career in digital or analog domain. Designing any circuit , which should meet all your goals i.e. like timing , power etc. etc. , You need to start from scratch . "What work they actually do " is a question of infinite answers.
If you choose your career in VLSI , then you have choice of selecting two paths i.e. frontend , which is basically related to logic design , verilog coding etc. and Backend , which relates to optimizing your design , circuit designing , connectivity of your components , choosing correct components ... etc. etc. ....