This talk describes a conjectured combinatorial interpretation for the higher q,t-Catalan numbers introduced by Garsia and Haiman, which arise in the theory of Macdonald polynomials. We define combinatorial statistics on lattice paths generalizing those proposed by Haglund and Haiman for the original q,t-Catalan numbers. We obtain various summation formulas, bijections, and recursions relating the new statistics. A third statistic occurs naturally in this context, leading to the introduction of three-variable Catalan numbers.