With the inherent benefits, such as, better cell coverage and higher area throughput, extra-large scale massive multiple-input multiple-output (MIMO) has great potential to be one of the key technologies for the next generation wireless communication systems. However, in practice, when the antenna dimensions grow large, spatial non-stationarities occur and users will only see a portion of the base station antenna array, which we call visibility region (VR). To assess the impact of spatial non-stationarities, in this paper, we investigate the uplink transmission of extra-large scale massive MIMO systems by considering VRs. In particular, we first propose a subarray-based system architecture for extra-large scale massive MIMO systems. Then, tight closed-form uplink spectral efficiency (SE) approximations with linear receivers are derived. With the objective of maximizing the achievable SE, we also propose schemes for the subarray phase coefficient design. In addition, based on the obtained ergodic achievable SE approximations, two statistical channel state information (CSI)-based greedy user scheduling algorithms are developed. Our results indicate that the statistical CSI-based greedy joint user and subarray scheduling algorithm collaborating with the on-off switch-based subarray architecture is a promising practical solution for extra-large scale massive MIMO systems.