Standard statistical analysis is often challenged by newly emerging issues and various complex features of data arising from practice. We are frequently faced with high-dimensional, complex structured, "imperfect" data that cannot be analyzed directly with standard methods. Data may be "imperfect" due to the presence of missing values and/or imprecise measurements which are pervasive in many settings. It is well known that ignoring these features in statistical analyses often leads to severely misleading results. Although there has been rapid development in the analysis of such data in recent years, many challenging problems still remain unexplored. In this talk, I will first briey review some modeling and inference issues concerning data with missing observations or measurement error, and then discuss in detail a marginal method for handling high-dimensional correlated data which are subject to missingness and measurement error.