The topic of arrangements of lines and points is a long studied one, going back at least to the times of Pappus in antiquity. A question known as the Orchard Problem posed at the beginning of the 19th century concerns existence of certain arrangements with prescribed incidences relating the lines and points. It has prompted a lot of research in combinatorics, algebra and geometry. After discussing the original problem and its solutions in detail, I will pass to some variations involving colored points and lines and generalizations to fields of definition other than the real numbers. Szemberg will also explain how combinatorial extremality for line arrangements comes up in very recent problems in commutative algebra and algebraic geometry.