Shigefumi Mori attended Kyoto University from where he received his B.A. in 1973, M.A. in 1975, and doctorate in 1978. He was visiting professor at Harvard during 1977-1980, at the Institute for Advanced Studies from 1981-82, at Columbia University from 1985-87, and the University of Utah for several periods. Mori research focuses on the birational geometry of algebraic varieties. One of his main results is the 3-dimensional flip theorem, which established the 3-dimensional birational classification theory based on the work of M. Reid, X. Benveniste, Y. Kawamata, V. Shokurov, J. Kollár, Y. Miyaoka and others. He is currently interested in a fine classification of certain threefold structures, including flips, divisorial contractions, and Q-conic bundles. Mori was awarded a Fields Medal at the 1990 International Congress in Kyoto in Japan. Mori is also President of the International Mathematical Union (IMU) until the end of 2018. Abstract: In my talk I will present my personal views on the area around my research; I have been studying algebraic varieties through rational curves on them. After I encountered a notion called an extremal ray, I became attracted to the biregular classification of special varieties, the minimal model program, and furthermore to a general theory of higher dimensional birational classification. I will present them touching some of the recent developments to a wider audience including algebraic geometers. The colloquium will be livestreamed from the ICTP website. Light refreshments will be served after the event.