I'll address the fundamentals of Cloud Computing and Virtualization. The types of cloud computing deployment models and their relationship with the responsibility of the users are developed. The fundamentals of digital criminal investigation applied to Cloud Computing are discussed, and the most significant challenges are presented to criminal investigation and forensic sciences in this type and digital environment. The implications of Virtualization used in Cloud Computing in Criminal Investigation and Forensic Science are discussed. The paradigm case of Nested Virtualization technology is presented as an obstacle to Criminal investigation and forensic investigation. In cases of criminal investigations in traditional environments, it is common practice for computer expertise to turn off the equipment and make a copy of the disks that will be analysed later in the laboratory. This is unfeasible in a cloud computing environment, due to the large storage capacity, legal issues, geographic distribution and data control, which may vary depending on the model of service contracted. In addition, lack of physical access to data collection and lack of control over the system make information acquisition a challenging task for cloud expertise. Therefore, forensic computing has been restructured, bringing new techniques, solutions and research methods, giving rise to cloud forensics or expertise in the cloud. Thus, the so-called Forensic as a Service (FaaS) is dedicated to solving the security challenges inherent in the cloud environment. In this paper we will analyse some of these challenges.