•The challenges and bottlenecks arising due to batch chromatography are identified.•Merits of continuous multi-column chromatography are provided.•The modelings and technologies currently available for the continuous chromatography are summarized.•The control strategy and gaps for implementation of continuous chromatography are described. The potential of continuous bioprocessing is hindered by the bottlenecks of chromatography processing, which continues to be executed in batch mode. Highlighting the critical drawbacks of batch chromatography, this review underscores the transition that the industry has made by implementing continuous upstream process without devising a working model for downstream chromatography operations. Even though multitude of process development initiatives have commenced, the review emphasizes the first principle models of chromatography on which these initiatives are built. Various models of continuous chromatography, which are essential, but not limited to multi-column systems, employed to congeal a unified process are reviewed. Advancements made by several mechanistic models and simulations to maximize productivity and performance are described, in an attempt to provide the integral tools. The modeling tools can be used for development of a strong model based control strategy and can be embedded into the continuous chromatography framework. The review addresses the limitations and challenges of the current modeling methods for development of robust mechanistic modeling and efficient unit operation platform in continuous chromatography. Display omitted