In this talk I first discuss some general properties of Unified Dark Matter (UDM) models. Using as an example models with an affine equation of state (EoS) I show how in general UDM models need to be extremely close to the standard LCDM model in order to be viable. The main problem is that the effective speed of sound - governing the Jeans length of the perturbations - needs to be extremely small, otherwise perturbations become incompatible with CMB and matter power spectra. In the second part of the talk I show how this problem can be avoided by UDM models with a fast transition. I will then introduce specific models and show that - for a wide range of parameter values - UDM models with a fast transition can fit the CMB and matter power spectra. I will end the talk discussing some work in progress.