For deployment flexibility and device lifetime prolonging, energy harvesting communications have drawn much attention recently, which however, encounter energy domain randomness in addition to the channel state randomness and traffic load randomness. The three-dimensional randomness makes the resource allocation problem extremely difficult. To resolve this, we exploit the inherent correlations of energy arrival and information. The correlations include self correlations of energy profiles and mutual correlations between energy and information in both time and spatial domains. The correlations are explicitly explained followed by a state-of-art survey. Candidate mechanisms exploiting the correlations for the ease of resource allocation are introduced along with some recent progress. Finally, a case study is presented to illustrate the performance of the proposed algorithm.