Today’s data-driven, electronic financial markets, wherein highly automated and, often, high frequency trading has become the norm for major participants, present significant technical challenges that complicate effective monitoring of their most fundamental functions, trade and the price discovery. Though regulators are implementing new surveillance systems capable of capturing all necessary market data to describe the details of market events, the fact that markets are fundamentally "complex systems" often undermines the use of conventional assessment techniques. The research work underlying this dissertation provides new approaches for analyzing financial markets that can help overcome these problems and demonstrates how each can be used to better understand the state of the market’s trading and price discovery processes. These approaches utilize adaptations of methods employing data visualizations, Markov State modeling, and agent based simulations that have been more commonly used in other fields.The occurrence of abnormal pricing anomalies in today’s complex markets has particularly intensified the demand for better monitoring and assessment, as it is crucial for regulators to be able to work to protect orderliness in markets and, thus, build confidence for both the industry and the public. These anomalies are transient, unique events that suddenly and unexpectedly take place in markets which are fundamentally complex systems environments with large numbers of participants each having their own, individual, ever-adapting views and decision-making processes. Much of the research effort in the dissertation is aimed at improving the capabilities of financial regulators and exchanges to better understand the precursors of such abnormal events and approach their investigation using methods that help overcome the effects of systematic complexities inherent in today’s data intensive markets.Through examination of financial markets as complex systems designed to support efficient and fair trade and pricing, this work has focused on untangling behavioral complexities by demonstrating how to apply techniques used in engineering that are well suited for the study of such systems. By breaking down the complexities based on the desired tasks and objectives, this work shows how issues arising from imaginary, periodic, and combinatorial complexities can be managed by using visual analytical techniques, Markov anomaly detection, and agent-based simulation. Through the use of such tools, regulators and exchanges can not only improve their analysis of markets post an event of interest, such as a "Flash Crash", but, also, analyze behaviors peri- and pre-events of interest.