Simultaneous localization and mapping (SLAM) has attracted considerable research interest from the robotics and computer-vision communities for >30 years. With steady and progressive efforts being made, modern SLAM systems allow robust and online applications in real-world scenes. We examined the evolution of this powerful perception tool in detail and noticed that the insights concerning incremental computation and temporal guidance are persistently retained. Herein, we denote this temporal continuity as a flow basis and present for the first time a survey that specifically focuses on the flow-based nature, ranging from geometric computation to the emerging learning techniques. We start by reviewing two essential stages for geometric computation, presenting the de facto standard pipeline and problem formulation, along with the utilization of temporal cues. The recently emerging techniques are then summarized, covering a wide range of areas, such as learning techniques, sensor fusion, and continuous-time trajectory modeling. This survey aims at arousing public attention on how robust SLAM systems benefit from a continuously observing nature, as well as the topics worthy of further investigation for better utilizing the temporal cues.