This paper is a survey on the emerging theory of truncated Toeplitz operators. We begin with a brief introduction to the subject and then highlight the many recent developments in the field since Sarason’s seminal paper  from 2007.
Copyright © 2013 Springer. This book chapter first appeared in Blaschke Products and their Applications.
The definitive version is available at: http://www.springer.com/mathematics/analysis/book/978-1-4614-5340-6?detailsPage=chapter
Ross, William T., and Stephan Ramon Garcia. "Recent Progress on Truncated Toeplitz Operators." In Blaschke Products and Their Applications, 275-319. United States: Spring, 2013.
Ross, William T. and Garcia, Stephan Ramon, "Recent Progress on Truncated Toeplitz Operators" (2013). Math and Computer Science Faculty Publications. 6.