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This paper provides an in-depth review of computation offloading algorithms within replicated fog computing environments, a critical area for modern distributed systems. It delineates the foundational concepts of fog computing and data replication, exploring their architectures, characteristics, and inherent challenges. The paper then systematically examines various offloading mechanisms and objectives, categorizing state-of-the-art algorithms, including optimization-based, machine learning-driven, and dynamic resource management approaches. A significant focus is placed on the complex interplay between offloading and replication, particularly concerning data consistency, fault tolerance, resource heterogeneity, and security. Through an analysis of real-world applications and identified research gaps, this review aims to serve as a foundational resource for PhD researchers, guiding future investigations into more robust, efficient, and intelligent offloading strategies in highly dynamic and resource-constrained fog environments.