As an ongoing problem, there are a great many ways to lose empire/(or main faction; empire faction for short) standings, but very few ways to gain them; for instance:
You lose empire standings for failing a mission, but do not gain empire standings for completing a mission (except for storylines). You lose empire standings for destroying their ships, but do not gain standings with the opposing empire.
Sometimes a standings hit for sinking a ship is low; other times it is quite high, with no explanation or warning for why that is.
Storyline missions result in derived standings losses with other empire factions; the only source of empire standings gains without derived empire standings losses is epic arcs.
In addition, there is no way to gain CONCORD standings; only to lose them.
As a general note, it gets harder to gain standings, and easier to lose them, the higher the standings become.
Like security status, low empire standings can get your ship blown up; unlike security status, you can’t turn in tags or otherwise buy you way out of low empire standings.
Taking together, this makes it quite difficult to increase standings, and quite easy to lose them. I hope that CCP fixes this problem. Giving derived standings with the faction(s) opposing the faction whose ships you sunk (in the same fashion as the Trig/EDENCOM derived standings effects) would be quite helpful. Also, giving small amounts of empire standings to those who complete regular missions for a corporation within that empire would be beneficial. CONCORD standings could be gained from killing pirates. The method of the past, where standings got harder and harder to gain as they increased, and it was hard to gain standings with all factions, may have made sense when mission running was one of the most profitable activities in the game, but, now that that has changed, making gaining standings easier would be balanced.