Since 1998, Chung has been the Paul Erdős Professor in Combinatorics at the University of California, San Diego (UCSD).

After working at Bell Laboratories and Bellcore for nineteen years, she joined the faculty of the University of Pennsylvania as the first female tenured professor in mathematics.

After high school, Chung entered the National Taiwan University (NTU) to start her career in mathematics formally.

There she obtained the highest score in the qualifying exam by a wide margin, catching the attention of Herbert Wilf, who would eventually become her doctoral advisor.

The same year she received her Ph.D. and started working for the Mathematical Foundations of Computing Department at Bell Laboratories in Murray Hill, New Jersey.

The position at Bell Laboratories was an opportunity to work with other excellent mathematicians, but also it contributed to her mathematical world powerfully.

In 1974, Fan Chung graduated from the University of Pennsylvania and became a member of Technical Staff working for the Mathematical Foundations of Computing Department at Bell Laboratories in Murray Hill, New Jersey.

After twenty years of work at Bell Laboratories and Bellcore, Chung decided to go back to the University of Pennsylvania to become a professor of mathematics.

As she wrote in "Graph Theory in the Information Age", Chung's life was profiled in the 2017 documentary film Girls who fell in love with Math.

During that time, they became close friends and published many joint papers in graph theory, eventually marrying in 1983.

Her work initiated a geometric approach to spectral graph theory with connections to differential geometry.

This book became a standard textbook at many universities and is the key to study spectral graph theory for many mathematics students who are interested in this area.

Her work provides a solid framework for quantitative and rigorous analysis for modeling and analyzing large complex networks.

[14] The book gave a well-structured exposition for using combinatorial, probabilistic, spectral methods as well as other new and improved tools to analyze real-world large information networks.

The notion of quasi-randomness has been extended to many other combinatorial structures, such as sequences, tournaments, hypergraphs and graph limits.

In a series of works with Paul Erdős, Chung determined the sizes and structures of unavoidable graphs and hypergraphs.