<p>Global warming and the utilization of greenhouse gases have become a matter of worldwide concern. Porous adsorbents have emerged as core materials for effectively capturing CO₂ and its isotopes. Flexible metal–organic frameworks (MOFs) stand out from traditional rigid adsorbents due to their unique structural flexibility and dynamic behavior. Owing to these characteristics, flexible MOFs have emerged as highly promising materials for CO₂ adsorption and separation. Moreover, the high working capacity and excellent selectivity of flexible MOFs confer significant advantages for CO₂ capture applications. They are expected to reduce energy consumption during adsorption–desorption cycles, positioning them as a promising new adsorbent. This review offers an overview of the dynamic behaviors of CO₂ adsorption by flexible MOFs. Furthermore, we summarized the cutting-edge achievements in adjusting gating pressure, adsorption hysteresis loops, and CO₂ affinity through ligand engineering, regulating the metal node, and functionalizing the pore environment. The challenges encountered with the material during actual carbon capture were discussed. Finally, an in-depth prospect is provided to promote the application of these materials in low-carbon energy and the high-value utilization of CO₂ and its isotopes.</p>