Carbon hydrocarbon compounds, especially low-carbon hydrocarbons (C1–C3), are vital raw materials in the petrochemical industry, but their efficient separation has great challenges due to their similar molecular structures and properties. In contrast to traditional low-temperature distillation and absorption separation technologies, selective adsorption employing porous materials as adsorbent has the advantages of low energy consumption, high efficiency, and high selectivity, indicating broad application possibilities in the field of low-carbon hydrocarbon separation. In this paper, the recent progress in the separation and purification of hydrocarbon mixtures by means of the two kinds of porous materials (metal–organic frameworks and molecular sieves) that have been widely used in recent years is reviewed, including purification of methane and separation of ethylene/ethane, propylene/propane, and some high-carbon hydrocarbon isomers. The structure–activity relationships between their chemical composition, structural characteristics, and separation performance are discussed to understand the separation mechanism. In conclusion, the issues encountered in the application of metal–organic frameworks and molecular sieves in the separation of low-carbon hydrocarbons are discussed in light of the current context of “carbon neutrality”.