In this review, we present our recent first principles studies on the sequential H₂ dissociative chemisorption and H desorption on the Pt_n and Pd_n clusters (n=2-9, 13). Upon full saturation by H atoms, the calculated H₂ dissociative chemisorption energy and H desorption energy on Pt₁₃ and Pd₁₃ clusters are similar to the corresponding values on smaller close-packed clusters. Indeed, the catalytic performances of these subnano clusters do not vary significantly with the particle sizes or shapes. Instead, they are dependent on the surface metal atoms which can be accessed by H atoms. In addition to the coverage dependency of the H₂dissociative chemisorption and H sequential desorption energies, the phase transition of both Pt₁₃ and Pd₁₃from the icosahedral to fcc-like structures at certain H coverage was also investigated.