As astrophysicists, we are used to extracting physical information from the observations. The usual procedure is to propose a parametric physical model to explain the observations and use the observations to infer the values of the parameters. However, in our noisy and ambiguous universe, the solution to the inference problem is usually non-unique or diffuse. For this reason, it is important that our inversion techniques give reliable results. In this talk I present a few recent results (dusty tori of AGN, magnetic fields in central stars of planetary nebulae, oscillations of coronal loops, signal detection) in which our group is applying Bayesian ideas to extract information from the observations.