Appears in collection : Colloque Scientifique International Poincaré 100

This talk will explain the question that Poincaré asked in 1905 that became known as the Poincaré Conjecture and sparked so much work in the following 100 years. I will explain the background material about surfaces that motivated and guided Poincaré and then explain what his this question. I will then briefly describe the mathematics that arose out of attempts to resolve the question and the method of solution foud by Perelman in 2002.