[dogma1138]

I'm not sure why this is being downvoted, it's technically correct (tho I'm not sure if it was in good faith) the observations don't explicitly require Dark Matter, it's just currently the most likely answer given the theoretical frameworks and observational evidence we have.

There are essentially 3 (or 2.5) explanations, that we have (a lot of) missing mass, that we don't understand gravity or that we don't understand spacetime.

Most theories revolve around the missing mass part this includes all possible theoretical candidates for Dark Matter from both within and beyond the standard model, overall a single candidate or a combination of a few likely ones seems to fit our observations the most.

Modified Gravity; these theories actually have gotten plenty of attention in the 80's and 90's but the problem is that most of them don't fit observations especially modern ones like the bullet cluster and gravitational waves, most of them aren't relativistic (or don't have a relativistic formulation) and they overall suck at predicting everything else including the formation of galaxies and stars in the first place.

"Modified Spacetime"; mostly relegated to the dark corners of the web and to pseudo scientific forums technically possible but I haven't seen anything that comes close to being an actual theory as in having an actual mathematical basis. They basically revolve around various possible ways of affecting spacetime curvature, basically if you could curve spacetime without out mass to the same extent as say the earth's mass does you'll technically will end up with the same gravity well. The more "serious" of these tend to revolve around various attempts at gauge gravity.

I usually consider the "Modified Spacetime" as being an offshoot of Modified Gravity theories.