We review inference methods for analyzing incomplete data with focus on interval censored data. For nonparametric analysis, two estimation approaches are examined. Self-consistency can be viewed as an extension of the method of moment by imputing incomplete information by its expected value. The other is the nonparametric likelihood estimation. We also introduce three popular regression models, namely the proportional hazards model, accelerated failure time model, and proportional odds model. These models contain unknown nuisance functions and different smoothing techniques are employed to handle them in the estimation procedure. The thesis focuses on point estimation so that second ordered properties are not investigated.