Topology forms a cornerstone in modern condensed matterand statistical physics, offering a new framework to classify thephases and phase transitions beyond the traditional Landauparadigm. However, it is widely believed that topological propertiesare destroyed when the bulk energy gap closes, making it highlynontrivial to consider topology in gapless quantum critical systems.To address these challenges, recent advancements have sought togeneralize the notion of topology to systems without a bulk energygap, including quantum critical points and critical phases, collectivelyreferred to as gapless symmetry-protected topological states.Extending topology to gapless quantum critical systems challenges thetraditional belief in condensed matter physics that topological edgestates are typically tied to the presence of a bulk energy gap.Furthermore, it suggests that topology plays a crucial role inclassifying quantum phase transitions even if they belong to the sameuniversalityfundamentally enriching thetextbookclass,understanding of phase transitions. Given its importance, here wegive a pedagogical talk of the current progress of topological physicsin quantum critical systems. We introduce the topological propertiesof quantum critical points and generalize them to stable criticalphases, both for noninteracting and interacting systems. Additionallywe discuss further generalizations and future directions, includinghigher dimensions, nonequilibrium phase transitions, and realizationsin modern experiments.