I will explain how several different moduli spaces of bundles on a smooth projective curve have abelian motives. Our starting point is a formula for the motive of the stack of vector bundles on the curve in Voevodsky's category of motives with rational coefficients. I will then explain how conservatively properties for abelian motives can be harnessed to obtain motivic formulae and provide motivic lifts of known cohomological phenomena, such as chi-independence and mirror symmetry. This is joint work with Simon Pepin Lehalleur.