Reconfigurable intelligent surfaces (RISs) have attracted great attention as a potential beyond 5G technology. These surfaces consist of many passive elements of metamaterials whose impedance can be controllable to change the phase, amplitude, or other characteristics of wireless signals impinging on them. Channel estimation is a critical task when it comes to the control of a large RIS when having a channel with a large number of multipath components. In this paper, we propose a novel channel estimation scheme that exploits spatial correlation characteristics at both the massive multiple-input multiple-output (MIMO) base station and the planar RISs, and other statistical characteristics of multi-specular fading in a mobile environment. Moreover, a novel heuristic for phase-shift selection at the RISs is developed, inspired by signal processing methods that are effective in conventional massive MIMO. Simulation results demonstrate that the proposed uplink RIS-aided framework improves the spectral efficiency of the cell-edge mobile users substantially in comparison to a conventional single-cell massive MIMO system.