Explore the evolution and significance of motivic cohomology in this 45-minute lecture by Marc Levine, presented at the International Mathematical Union. Gain insights into the parallels between motivic and singular cohomology, and understand its role within motivic stable homotopy theory. Discover recent developments in the field, including cycles with modulus, Chow-Witt theory, and motivic filtrations on p-adic K-theory. Delve into potential future directions for this mathematical discipline. Access accompanying slides for a comprehensive visual aid to enhance your understanding of this complex topic.