Welding is a major manufacturing process that joins two or more pieces of materials together through heating/mixing them followed by cooling/solidification. The goal of welding manufacturing is to join materials together to meet service requirements at lowest costs. Advanced welding manufacturing is to use scientific methods to realize this goal. This paper views advanced welding manufacturing as a three step approach: (1) pre-design that selects process and joint design based on available processes (properties, capabilities, and costs); (2) design that uses models to predict the result from a given set of welding parameters and minimizes a cost function for optimizing the welding parameters; and (3) real-time sensing and control that overcome the deviations of welding conditions from their nominal ones used in optimizing the welding parameters by adjusting the welding parameters based on such real-time sensing and feedback control. The paper analyzes how these three steps depend on process properties/capabilities, process innovations, predictive models, numerical models for fluid dynamics, numerical models for structures, real-time sensing, and dynamic control. The paper also identifies the challenges in obtaining ideal solutions and reviews/analyzes the existing efforts toward better solutions. Special attention and analysis have been given to (1) gas tungsten arc welding (GTAW) and gas metal arc welding (GMAW) as benchmark processes for penetration and materials filling; (2) keyhole plasma arc welding (PAW), keyhole-tungsten inert gas (K-TIG), and keyhole laser welding as improved/capable penetrative processes; (3) friction stir welding (FSW) as a special penetrative low heat input process; (4) alternating current (AC) GMAW and double-electrode GMAW as improved materials filling processes; (5) efforts in numerical modeling for fluid dynamics; (6) efforts in numerical modeling for structures; (7) challenges and efforts in seam tracking and weld pool monitoring; (8) challenges and efforts in monitoring of keyhole laser welding and FSW; and (9) efforts in advanced sensing, data fusion/sensor fusion, and process control using machine learning/deep learning, model predictive control (MPC), and adaptive control.