Cloud computing has been adopted very rapidly by organizations with different businesses and sizes, the use of cloud services is rising at an unparalleled rate these days especially IaaS services as cloud providers offer more powerful resources with flexible offerings and models. This rapid adoption opens new surface attacks to the organizations that attackers abuse with their malware to take advantage of these powerful resources and the valuable data that exist on them. Therefore for organizations to well defend against malware attacks they need to have full visibility not only on their data centers but also on their resources hosted on the cloud and don't take their security for granted. This paper discusses and aims to provide the best approaches to achieve continuous monitoring of malware attacks on the cloud along with their phases (before, during, and after) and the limitations of today's available techniques suggesting needed developments. Logging and forensics techniques have always been the cornerstone of achieving continuous monitoring and detection of malware attacks on-premises, this paper defines the best methods to bring loggings and forensics to the cloud and integrate them with on-premises visibility, thus achieving the full monitoring over the whole security posture of the organization assets whether they are on-premises or on the cloud.