In air traffic management, the primary goal is the safety and efficiency of airspace operations under the responsibility of air traffic controllers (ATCs). With the growing demand of air traffic, it becomes critical to develop advanced techniques to support the decisions made by ATCs, which include control and monitoring of air traffic. To reduce the workload on ATCs in both control and monitoring, this thesis focuses on the development of decision supporting tools for (i) aircraft conflict resolution in en-route airspace and (ii) conformance monitoring in terminal airspace. The first part of this thesis focuses on the development of a data-driven conflict resolution tool which can aid the decision-making process of ATCs for air traffic conflict resolution. The decision-making process can be viewed as a system that takes conflict situations as input and generates corresponding conflict resolution methods as output. That is, each conflict can be represented as a tuple of (Conflict Situation, Resolution Methods). To construct a conflict data in this form from air traffic surveillance data, we first need to label each conflict situation, or identify resolution methods (outputs) used for the conflict situation. The key idea is that any complex maneuvers can be modeled as a sequence of simple or primitive motions, called intents. Using the domain knowledge obtained from flight data and the intent inference algorithm, a framework for the detection and characterization of aircraft resolution maneuvers is proposed to identify resolution types and resolution parameters. Based on the knowledge extracted from the constructed conflict data with the features representing conflict situations (or inputs), a classification model is designed which determines the resolution type for every two-aircraft conflict in the airspace. In addition to predicting the resolution type, the proposed conflict resolution algorithm can also suggest appropriate resolution parameters for the guaranteed safe separation. The combination of the resolution type prediction model and resolution parameter suggestion model can sufficiently and safely resolve any two aircraft conflict. The second part of the thesis is for the development of a conformance monitoring methodology for the current and future time, to help enhance the situational awareness of ATCs. To predict the future states of an aircraft, a trajectory prediction framework is developed by combining a data-driven prediction model, which generates expected states of an aircraft learned from flight data, and a physics-based prediction method, which incorporates the current motion of an aircraft. Since the estimated or predicted states of an aircraft are stochastic, a stochastic version of anomaly detection and prediction algorithm for sequentially updated aircraft trajectories is developed using a smooth approximation for numerical integration. All the proposed methods are demonstrated with real flight data to show their potentials as decision supporting tools that can help reduce the workload on air traffic controllers and enhance the safety of air traffic operations.