In my talk I will review our recent developments in calculating the strong coupling expansion of specific observables in N=2 and N=4 superconformal Yang-Mills theories. These observables can be written as determinants of semi-infinite matrices, the generalizations of the famous Tracy-Widom distribution. By exploiting this relationship we developed an efficient method to compute their strong coupling expansion, which is an asymptotic series. This necessitates the involvement of non-perturbative corrections, which we also determine together with their intriguing resurgence relations.