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The discovery and optimization of porous materials, particularly metal–organic frameworks (MOFs), are critical for advancing a range of applications, including gas storage, separation, catalysis, and energy technologies. Traditional molecular modeling methods such as Monte Carlo simulations, molecular dynamics (MD), and quantum based method such as density functional theory (DFT), has long provided valuable insights into material behavior but is often limited by high computational costs, scalability challenges, and the vast complexity of material design spaces. Machine learning has addressed some of these limitations but often requires extensive datasets, which introduce new challenges in computational efficiency. Active learning (AL) has emerged as a promising approach, offering a data-efficient framework to address these limitations. AL minimizes computational demands while maintaining high predictive accuracy by iteratively refining surrogate models and prioritizing the acquisition of the most informative data points. This review presents AL across the major tasks in MOF research: single- and multicomponent adsorption (including universal, cross-adsorbate surrogates built via alchemical-to-real transfer), diffusion and transport, electronic-structure/property prediction, experiment-in-the-loop optimization, and the training of machine-learned interatomic potentials (MLIPs). Case studies show AL recovering full isotherms and mixture landscapes with a fraction of grand canonical Monte Carlo labels, cutting MD trajectories for diffusivity, curating balanced sets for band gaps and adsorption targets, and enabling near-DFT MLIPs that capture rare events and phase changes through enhanced-sampling or uncertainty-biased data acquisition. Looking forward, we outline a path to end-to-end discovery that couples AL with generative MOF models, graph neural networks, foundational MLIPs, and that integrates experimental feedback. Together, these advances move AL beyond label efficiency toward reliable, scalable discovery workflows for gas storage, separations, catalysis, and stability screening in MOFs.