The classical model of percolation is the following: for a given parameter $p\in [0,1]$, each edge of the graph $\mathbf{Z}^d$ is kept (resp.\ removed) with probability $p$ (resp.\ $1-p$), independently of each other. It exhibits a phase transition, i.e., there exists a critical parameter $p_c$ such that if $p<p_c$ then a.s.\ all the connected components of the random graph defined above are bounded, whereas if $p>p_c$ then a.s.\ there exists a unique infinite connected component in this graph. This phase transition is sharp, in the sense that if $p<p_c$, the probability that the origin of the graph is connected to a vertex at distance $n$ not only converges to $0$, but it goes to $0$ exponentially fast with $n$. This fundamental result is known since the 80's thanks to a paper by Menshikov and a paper by Aizenman and Barsky. In this talk we will present a new proof of this result given by Duminil-Copin, Raoufi, and Tassion and using decision trees. Their approach is very robust and can be adapted to many variants of the percolation model for which the sharpness of the phase transition was not proved before.