Flexible metal–organic frameworks (MOFs) offer unique opportunities due to their dynamic structural adaptability. This review explores the impact of flexibility on gas adsorption, highlighting key concepts for gas storage and separation. Specific examples demonstrate the principal effectiveness of flexible frameworks in enhancing gas uptake and working capacity. Additionally, mixed gas adsorption and separation of mixtures are reviewed, showcasing their potential in selective gas separation. The review also discusses the critical role of the single gas isotherms analysis and adsorption conditions in designing separation experiments. Advanced combined characterization techniques are crucial for understanding the behavior of flexible MOFs, including monitoring of phase transitions, framework–guest and guest–guest interactions. Key challenges in the practical application of flexible adsorbents are addressed, such as the kinetics of switching, volume change, and potential crystal damage during phase transitions. Furthermore, the effects of additives and shaping on flexibility and the “slipping off effect” are discussed. Finally, the benefits of phase transitions beyond improved working capacity and selectivity are outlined, with a particular focus on the advantages of intrinsic thermal management. This review highlights the potential and challenges of using flexible MOFs in gas storage and separation technologies, offering insights for future research and application.