The Coupled Model Intercomparison Project (CMIP) simulates standardized experiments spanning historical, future, and hypothetical conditions, to better understand the Earth system's evolution. Systematic biases remain a persistent limitation of coupled climate models. Within the framework of the CMIP, successive model generations have increased in complexity, resolution, and representation of Earth system processes, yet many long-standing biases remain across atmosphere, ocean, land, and cryosphere components, and their interactions and feedbacks. In this literature review, we identify the characteristics of key systematic biases in coupled models from CMIP6 and earlier CMIP phases to aid future comparisons to CMIP7. We introduce results of a community survey, designed to prioritize diagnostics for the Rapid Evaluation Framework (REF), and use these diagnostics for our review. Biases are shown to be interconnected across the Earth system, via sea surface temperature distributions, ENSO patterns, AMOC´s large scale transport biases, sea ice, the carbon cycle and radiation fluxes among others, with impacts on the Earth system response through metrics such as the Transient Climate Response and Equilibrium Climate sensitivity. The physical mechanisms underlying these biases and strategies to reduce them are presented, including improved parameterizations, increased resolution, and enhanced coupling among Earth system components. This review synthesizes current understandings of systematic biases across the Earth System, providing an assessment of biases in a set of critical diagnostics. In addition we provide a perspective on the advances in physical processes, higher resolution modelling frameworks, and targeted experiments and model evaluation frameworks expected in CMIP7. This review serves as an overview for end users, those new to CMIP data and those looking to connect different aspects of the Earth system.