Schramm's Lemma had initially generated much hope in the study of critical percolation (and the attempt of proving p_c < p_u for non-amenable graph). In the light of a new proof from Tom Hutchcroft we might understand the reason for this failure. Nevertheless Schramm's Lemma remains a powerful tool to obtain exponential decay and we'll present an application to biased random walk on the supercritical cluster or Bernouilli percolation.