Simultaneous Localization and Mapping is now widely adopted by many applications, and researchers have produced very dense literature on this topic. With the advent of smart devices, embedding cameras, inertial measurement units, visual SLAM (vSLAM), and visual-inertial SLAM (viSLAM) are enabling novel general public applications. In this context, this paper conducts a review of popular SLAM approaches with a focus on vSLAM/viSLAM, both at fundamental and experimental levels. It starts with a structured overview of existing vSLAM and viSLAM designs and continues with a new classification of a dozen main state-of-the-art methods. A chronological survey of viSLAM's development highlights the historical milestones and presents more recent methods into a classification. Finally, the performance of vSLAM is experimentally assessed for the use case of pedestrian pose estimation with a handheld device in urban environments. The performance of five open-source methods Vins-Mono, ROVIO, ORB-SLAM2, DSO, and LSD-SLAM is compared using the EuRoC MAV dataset and a new visual-inertial dataset corresponding to urban pedestrian navigation. A detailed analysis of the computation results identifies the strengths and weaknesses for each method. Globally, ORB-SLAM2 appears to be the most promising algorithm to address the challenges of urban pedestrian navigation, tested with two datasets.