  We study algebraic cycles on complex Gushel-Mukai (GM) varieties. We prove
the generalised Hodge conjecture, the (motivated) Mumford-Tate conjecture, and
the generalised Tate conjecture for all GM varieties. We compute all integral
Chow groups of GM varieties, except for the only two infinite-dimensional cases
(1-cycles on GM fourfolds and 2-cycles on GM sixfolds). We prove that if two GM
varieties are generalised partners or generalised duals, their rational Chow
motives in middle degree are isomorphic.
