Cloud computing provides services rather than products; where it offers many benefits to clients who pay to use hardware and software resources. There are many advantages of using cloud computing such as low cost, easy to maintain, and available resources. The main challenge in the Cloud system is how to obtain a highly secured system against attackers. For this reason, methods were developed to increase the security level in different techniques. This paper aims to review these techniques with their security challenges by presenting the most popular cloud techniques and applications. Homomorphic Encryption method in cloud computing is presented in this paper as a solution to increase the security of the data. By using this method, a client can perform an operation on encrypted data without being decrypted which is the same result as the computation applied to decrypted data. Finally, the reviewed security techniques are discussed with some recommendations that might be used to raise the required security level in such a system.