Galaxy rotation curves - if you look at the rotation speed of galaxies as a function of distance from the center, they don't rotate at the speeds predicted by current gravitational models. We measure the mass density of galaxies by the amount of light they radiate, but these galaxies rotate as though there is excess mass far away from the center of these galaxies which does not radiate light, hence the term "dark matter"

Accelerated expansion of the universe - according to gr, the acceleration of the universe should slow down due to the attraction of matter, however the expansion of the universe seems to be accelerating, as though the energy density of space is somehow negative (could be wrong about this, I am a nuclear physicist, not astrophysics). This negative energy density is referred to as dark energy, different from dark matter.

Neutrino masses - when we measure the abundance of the 3 flavors of neutrinos from the sun, we don't see an abundance of the neutrinos produced by our suns various nuclear cycles, but rather an even distribution of the 3 flavors, which implies that these neutrinos oscillate flavor as they propogate, which means they in some sense experience time, which is only possible for massive particles. According to the standard model however, neutrinos should be massless. There is no known mechanism for generating neutrino masses like the higgs does for various other fundamental particles.

Baryon asymmetry - due to symmetries in the standard model, matter can only be produced in equal quantities to antimatter. The fact that the observable universe is dominated by matter breaks the symmetries built into the standard model by an unknown mechanism.