We prove convergence to conformally covariant scaling limits for a family of observables in the critical 2D Ising model, including spins, energies, disorders and fermions. We also check that the limits satisfy fusion rules (a. k. a. Operator product expansions) as predicted by Conformal Field Theory. I will also explain how to apply these results to deduce convergence of Ising interfaces to SLE(3) variants in a general setting. Joint work with D. Chelkak and C. Hongler.