Coarse geometry is the study of large scale features of metric spaces. A central notion in coarse geometry is that of quasi-isometry. The study of coarse geometry of groups (with their word metrics), promoted by Gromov, had led to explosive developments. The aim of my talk will be to introduce and illustrate the concepts of quasi-isometry and quasi-isometric rigidity, the notion of word metrics on groups. If there is time, I will talk about quasi-isometric rigidity for lattices in semisimple Lie groups.