We develop a characterization of fading models, which assigns a number called logarithmic Jensen's gap to a given fading model. We show that as a consequence of a finite logarithmic Jensen's gap, approximate capacity region can be obtained for fast fading interference channels (FF-IC) for several scenarios. We illustrate three instances where a constant capacity gap can be obtained as a function of the logarithmic Jensen's gap. Firstly for an FF-IC with neither feedback nor instantaneous channel state information at transmitter (CSIT), if the fading distribution has finite logarithmic Jensen's gap, we show that a rate-splitting scheme based on average interference-to-noise ratio (inr) can achieve its approximate capacity. Secondly we show that a similar scheme can achieve the approximate capacity of FF-IC with feedback and delayed CSIT, if the fading distribution has finite logarithmic Jensen's gap. Thirdly, when this condition holds, we show that point-to-point codes can achieve approximate capacity for a class of FF-IC with feedback. We prove that the logarithmic Jensen's gap is finite for common fading models, including Rayleigh and Nakagami fading, thereby obtaining the approximate capacity region of FF-IC with these fading models. For Rayleigh fading the capacity gap is obtained as 1.83 bits per channel use for non-feedback case and 2.83 bits per channel use for feedback case. Our analysis also yields approximate capacity results for fading 2-tap ISI channel and fading interference multiple access channel as corollaries.