BASE is a multinational collaboration at the Antiproton Decelerator (AD) of CERN which aims at precise comparisons of the fundamental properties of antiprotons and protons. Such comparisons provide stringent tests of charge-parity-time reversal invariance which is the most fundamental symmetry in the Standard Model of particle physics. The BASE collaboration observed the first spin flips with a single trapped proton, measured the magnetic moment of the proton with a fractional precision at the ppm level, observed first single proton spin filps, and performed the first direct high-precision measurement of the magnetic moment of a single trapped proton. Our most recent value has a precision of 0.3 ppb, which outperforms previous Penning trap experiments by a factor of >9000. In addition BASE performed one of the most precise tests of CPT invariance with baryons, by comparing the antiproton-to-proton charge-to-mass ratio with a fractional precision of 69 parts in a trillion. Very recently we measured the magnetic moment of the antiproton with a fractional precision of 1.7 parts in a billion based on a newly invented two particle/three trap method and the observation of single spin transitions with a single trapped antiproton. These measurements improve previous best antiproton magnetic moment measurements by a factor of 3000 and also enabled us to set first ever constraints on the coupling of antiprotons to axion like dark matter.