A decade ago the problem of decoding algebraic-geometric codes looked hardly tangible and rather far from algebraic geometry. Both proved to be wrong. The break-through, started by Justesen during his visit to Moscow in 1988, last year reached the point of decoding algebraic-geometric codes up to half the designed minimum distance. This illustrious achievement is due to the work of many mathematicians, including Vladut, Skorobogatov, Larsen, Havemose, Elbrond Jensen, Hoholdt, Porter, Krachkovskii, Pellikaan, and Shen, the final result being obtained by Ehrhard, Feng, Rao, and Duursma. The algorithms we have now are both of reasonable complexity and rather easy to understand. However they do tangle several specifical difficulties of algebraic geometry nature. In this talk the principal points of these decoding algorithms will be described for the simplest example of the curve being the line, with the difficulties of the general case being pointed out on the way.