I'll chime in since I also worked in consulting for a long time (still do). It depends a lot on what vertical you get pulled into, but I'd say it's 50% luck and 50% you putting in the effort to develop and prove you have skills (including social ones) to get staffed on interesting projects. Many consultants never see more than conference rooms and the home office, but the parent commenter's experience also happens quite a bit. It's worth noting that in my experience the more advanced you get in your career the more likely you are to work only in a specific industry.