This dissertation is composed of three papers which address the problem of variable selection for models with missing data. In the first paper, we consider variable selection for generalized linear models with missing data, including missing covariate and/or response data. The second paper deals with variable selection in the Cox regression model with covariates missing at random. For the third paper, we consider jointly selecting fixed and random effects in mixed effect models. In all three papers, we calculate the maximum penalized likelihood estimates using the smoothly clipped absolute deviation (SCAD) and adaptive LASSO (ALASSO) penalty functions and propose a unified model selection and estimation procedure for use in the presence of missing data. The maximum penalized likelihood estimates are shown to posses consistency and sparsity properties and are asymptotically normal. A computationally attractive algorithm is developed which simultaneously optimizes the penalized likelihood function and penalty parameters. Particularly, we propose to use a model selection criterion, called the ICQ criterion, for selecting the penalty parameters. We show that the variable selection procedure based on ICQ consistently selects important covariates and/or fixed and random effects. The methodology is very general and can be applied to numerous situations involving missing data, from covariates missing at random in arbitrary regression models to nonignorably missing longitudinal responses and/or covariates to mixed effects models.