In recent years, there has been a dramatic change in attitude towards computers and the use of computer resources in general. Cloud and Edge computing have emerged as the most widely used technologies, including fog computing and the Internet of Things (IoT). There are several benefits in exploiting Cloud and Edge computing paradigms, such as lower costs and higher efficiency. It provides data computation and storage where data are processed, enables better data control, faster understanding and actions, and continuous operation. However, though these benefits seem to be appealing, their effects on computer forensics are somewhat undesirable. The complexity of the Cloud and Edge environments and their key features present many technical challenges from multiple stakeholders. This paper seeks to establish an in-depth understanding of the impact of Cloud and Edge computing-based environmental factors. Software and hardware tools used in the digital forensic process, forensic methods for handling tampered sound files, hidden files, image files, or images with steganography, etc. The technical/legal challenges and the open design problems (such as distributed maintenance, multitasking and practicality) highlight the various challenges for the digital forensics process.