Simultaneous localization and mapping (SLAM) is an active research topic in machine vision and robotics. It has various applications in many different fields such as mobile robots, augmented and virtual reality, medical imaging, image-guided surgery systems, and unmanned aerial vehicles (UAVs). The computational complexity of SLAM algorithms is very high. Therefore, in many applications, it is necessary to implement them in real-time on platforms with low power consumption and small sizes. This paper reviews the implementation and the performance of SLAM algorithms on various platforms. Although there are various review studies on SLAM algorithms, the studies assessing the hardware implementation of these algorithms are very limited. This study attempts to fill this gap. It is shown that using the hardware–software (HW/SW) co-design approaches over mere Software (SW) or hardware (HW) approaches is currently the primary option for implementing SLAM algorithms on hardware platforms. A combination of a hardware accelerator and a software approach increases the speed of the implementation as well as the performance and the speed of the algorithm. Also, dividing different parts of the algorithm according to the structure and the nature of the algorithm between hardware and software in the HW/SW co-design approaches reduces the resource consumption and the cost. Furthermore, the design of hardware-compatible algorithms is one of the most critical gaps in the implementation of SLAM algorithms on hardware platforms.