The NA62 experiment at CERN aims to search for new phenomena beyond the Standard Model, by measuring two of the theoretically cleanest kaon decays. Two phases can be distinguished in the NA62 physics programme. During the current short term phase (data taking completed in years 2007-8), the ratio R K = Γ(K + → eν e (γ))/Γ(K + → µν µ (γ)) of leptonic decay rates is studied, which tests the structure of weak interactions and lepton flavour universality. In the second phase (long term) the experiment will focus on the measurement of the branching ratio of the very rare kaon decay K + → π + νν with a 10% precision. In this paper, firstly the R K analysis is summarized, and the preliminary result R K = based on 40% of data collected in 2007 is discussed. Then a status report of the long term project is presented, including a discussion of the beam line, detectors, and the experimental strategy.Flavor Physics and CP Violation -FPCP 2010