Visual odometry and visual simultaneous localization and mapping aid in tracking the position of a camera and mapping the surroundings using images. It is an important part of robotic perception. Tracking and mapping using a monocular camera is cost-effective, requires less calibration effort, and is easy to deploy across a wide range of applications. This paper provides an extensive review of the developments for the first two decades of the twenty-first century. Astounding results from early methods based on filtering have intrigued the community to extend these algorithms using other forms of techniques like bundle adjustment and deep learning. This article starts by introducing the basic sensor systems and analyzing the evolution of monocular tracking and mapping algorithms through bibliometric data. Then, it covers the overview of filtering and bundle adjustment methods, followed by recent advancements in methods using deep learning with the mathematical constraints applied on the networks. Finally, the popular benchmarks available for developing and evaluating these algorithms are presented along with a comparative study on a different class of algorithms. It is anticipated that this article will serve as the latest introductory tool and further ignite the interest of the community to solve current and future impediments. © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.