Modern economic research emphasizes heterogeneity in various dimensions, such as individual preferences or firms’ technology. From an empirical perspective, the presence of unobserved heterogeneity (to the econometrician) creates challenging identification and estimation problems. In this proposal we explore these issues in a context where repeated observations are available for the same individual, and the researcher disposes of panel data. Most research to date adopts either of three approaches. One approach consists in modeling the distribution of unobserved heterogeneity, following a random-effects perspective (Chamberlain, 1984). Another approach looks for clever model-specific ways of differencing out the unobserved heterogeneity (Andersen, 1970, Honore and Kyriazidou, 2000). A more recent line of research relies on approximations that become more accurate when the number of observations per individual T gets large (Arellano and Hahn, 2006). Here we consider situations where T may be small, and the researcher does not restrict the distribution of the unobserved fixed effects. We will propose a new functional differencing approach which differences out the probability distribution of unobserved heterogeneity. This approach will generally be applicable in models with continuous dependent variables, emphasizing a possibility of point-identification of the structural parameters in those models. When outcomes are discrete, we will propose a nonlinear differencing strategy that delivers useful bounds on parameters in the presence of partial identification (Honore and Tamer, 2006).