This is an introductory talk about a new notion of BV functions on fractals, using the Sierpinski gasket and carpet and the Vicsek set as the prime examples. I will describe a semigroup approach recently developed in a joint work with Patricia Alonso-Ruiz, Fabrice Baudoin, Li Chen, Luke Rogers, Nageswari Shanmugalingam. This approach can be connected to the Distribution theory on PCF fractals developed earlier by Luke Rogers and Robert Strichartz. I also will talk how this notion of derivatives can lead to a new physics law on fractals, in a joint work with Eric Akkermans and Robert Strichartz.