Cloud computing is considered one of the most dominant paradigms in the Information Technology (IT) industry nowadays. It offers powerful processing and storage resources as on-demand services at reduced cost, and improved efficiency. It enables sharing computing physical resources among cloud computing tents and offers on-demand scaling with cost efficiency. However, with all of these services promising facilities and benefits, there are still a number of challenges associated with utilising cloud computing such as data security, abuse of cloud services, malicious insider and cyber-attacks. The target of this paper is to explore potential security issues related to securing cloud computing, highlight research directions and investigates various security challenges to cloud consumer and service providers. It divides cloud security and privacy threats into three main categories: threats to cloud service provider, attacks and threats to cloud physical infrastructure and threats to cloud customers.