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Leveraging on the reconfigurable intelligent surface (RIS) paradigm for enabling the next Internet of Things (IoT) and 6G era, this paper develops a comprehensive theoretical framework characterizing the performance of RIS-assisted communications in a plethora of propagation environments. We derive unified mathematical models for the outage probability and ergodic capacity of single and multiple-element RIS over Fox's H fading channel, which includes as special cases nearly all linear and non linear multi-path and shadowing fading models adopted in the open literature. For gleaning further insights, we capitalize on the algebraic asymptotic expansions of the H-transform to further analyze the outage probability and capacity at high signal-to-noise ratio (SNR) in a unified fashion. Asymptotic analysis shows two scaling rates of the outage probability at large average SNR. Moreover, by harnessing its tractability, the developed statistical machinery is employed to characterize the performance of multiple randomly distributed RIS-assisted communications over Fox's H fading channels. We show that there is a great potential to improve the outage performance and thereby the capacity when fewer RISs are deployed each with more reflecting elements.