Software-as-a-service (SaaS) is a type of software service delivery model which encompasses a broad range of business opportunities and challenges. Users and service providers are reluctant to integrate their business into SaaS due to its security concerns while at the same time they are attracted by its benefits. This article highlights SaaS utility and applicability in different environments like cloud computing, mobile cloud computing, software defined networking and Internet of things. It then embarks on the analysis of SaaS security challenges spanning across data security, application security and SaaS deployment security. A detailed review of the existing mainstream solutions to tackle the respective security issues mapping into different SaaS security challenges is presented. Finally, possible solutions or techniques which can be applied in tandem are presented for a secure SaaS platform.