regex and FSAs

I find current topics very interesting, and again, the way the course was structured for this material is fantastic. First we were shown that there is an equivalent NFSA to every regex. Then, we were shown that for every NFSA there is an equivalent DFSA. Then we were shown that we can construct an equivalent (I think? Havent yet seen the rigorous notes) regex from a DFSA, by "ripping" states and transitions out. So, every regex has an equivalent FSA.

I wonder how each of these different forms of representation are useful, and how they may be used in my further studis in compsci.