When I was in college more than 20 years ago there was a class where we designed our own transistors (with a lot of help from the course material), assembled those into logic gates and registers, assembled those into adders, multipliers, memories, etc., and finally implemented a function like a CRC calculator/checker. We then sent our designs to MOSIS and got a chip back. By far the coolest class I took.

Then I got into industry and saw that each of those steps is done by a different team of people, often at different companies. Most companies doing "chip design" today are buying off-the-shelf processors, system busses, memories, dma engines, network subsystems, sensor interfaces, etc. and just wiring them up. It's honestly kind of just, tedious now. The challenges have more to do with making sure those components are all mated up correctly than in doing any fun design work, at least for everyone on the team except the "chip architect." Working on the verification team is usually more interesting than on the design team on these kinds of projects (but don't tell the designers I said that).

I currently work for a company doing novel digital designs targeting FPGAs. There are still some off-the-shelf parts such as a PCIe, Ethernet, etc. blocks, but a good amount of the stuff I did in school, such as designing state machines, efficient data structures, and instruction sets. It's pretty fun.