Modern manufacturing needs to optimize the entire product lifecycle to satisfy the customer needs. The advancement of sensing technologies has brought a data rich environment for manufacturing and provide a great opportunity for real-time, proactive quality assurance. However, due to the lack of methods for analyzing heterogeneous types of data, the transformation of data to information and knowledge for effective decision making in manufacturing is still a challenging problem. In particular, functional variables can represent the in situ process conditions and rich product performance information, and are widely encountered in various manufacturing processes. In this dissertation, I will focus on modeling of manufacturing processes with in situ process (functional) variables, and integrating these functional variables and other measured variables for the manufacturing modeling. The modeling is explored by extracting informative features through the integration of multiple functional variables, functional variables and offline setting variables, and quantitative and qualitative quality variables. After an introduction in Chapter 1, three research tasks are investigated. First, a functional variable selection problem is studied in Chapter 2 to identify the significant functional variables as well as their features in a logistic regression model. A hierarchical non-negative garrote constrained estimation method is proposed. Second, the quality-process relationships for scalar offline setting variables, functional in situ process variables, and manufacturing quality responses are studied in Chapter 3. A functional graphical model that can integrate functional variables in a graphical model is proposed and investigated. Third, the quantitative and qualitative quality responses are jointly modeled with scalar offline setting variables and functional in situ process variables in Chapter 4. A functional quantitative and qualitative model is proposed and investigated. Finally, I summarize the research contribution and discuss future research directions in Chapter 5. The proposed methodologies have broad applications in manufacturing processes with functional variables, and are demonstrated in a crystal growth process with multiple functional variables (Chapter 2), a plasma spray process with multiple scalar and functional variables (Chapter 3), and an additive manufacturing process called fused deposition modeling with quantitative and qualitative quality responses (Chapter 4). / Ph. D.