We have investigated Langmuir films at the water surface using grazing-incidence diffuse X-ray scattering. We show that beyond structural parameters like the film thickness and density, diffuse scattering also gives access to phase transitions and elastic properties (surface tension and bending rigidity). We find that the surface tension measured with X-rays is consistent with the Wilhelmy plate measurements, at least for tilted phases. The bending rigidity is found to be on the order of 20 30kBT whatever the phase. The underlying molecular mechanisms are discussed using different models.