Structural reasons - somehow the world is set up in such way that something is mispriced. For example, implied volatility is over-priced because the institutional investors are forced to hedge big downside swings. These dislocations are usually very stable and will persist for a while.
Theoretical edge - for example, if two securities are supposed to converge at some point or have a theoretical relationship that is dislocated. For example, if you can buy a bond and an equity put on the same company with the same maturity in such way that the yield pays for your option. It's not a true arbitrage, but your chances of making money are better than average.
Regimes in general refer to the repetitive behavior of some market. A simple case could be "trend vs chop" or something like that.