The goal of this mostly introductory talk will be to illustrate some key concepts in mirror symmetry, by considering some of the simplest examples: Riemann surfaces of low genus. These examples will be a pretext to discuss the Strominger-Yau-Zaslow picture of mirror symmetry (according to which mirror pairs carry dual torus fibrations), as well as Kontsevich\'s homological mirror symmetry conjecture. I will also try to motivate the appearance of "wrapped" Fukaya categories in the open case.