The replication mechanism resolves some challenges with big data such as data durability, data access, and fault tolerance. Yet, replication itself gives birth to another challenge known as the consistency in distributed systems. Scalability and availability are the challenging criteria on which the replication is based upon in distributed systems which themselves require the consistency. Consistency in distributed computing systems has been employed in three different applicable fields, such as system architecture, distributed database, and distributed systems. Consistency models based on their applicability could be sorted from strong to weak. Our goal is to propose a novel viewpoint to different consistency models utilized in the distributed systems. This research proposes two different categories of consistency models. Initially, consistency models are categorized into three groups of data-centric, client-centric and hybrid models. Each of which is then grouped into three subcategories of traditional, extended, and novel consistency models. Consequently, the concepts and procedures are expressed in mathematical terms, which are introduced in order to present our models' behavior without implementation. Moreover, we have surveyed different aspects of challenges with respect to the consistency i.e., availability, scalability, security, fault tolerance, latency, violation, and staleness, out of which the two latter i.e. violation and staleness, play the most pivotal roles in terms of consistency and trade-off balancing. Finally, the contribution extent of each of the consistency models and the growing need for them in distributed systems are investigated.