  Deflectometry as a technical approach to assessing reflective surfaces has
now existed for almost 40 years. Different aspects and variations of the method
have been studied in multiple theses and research articles, and reviews are
also becoming available for certain subtopics. Still a field of active
development with many unsolved problems, deflectometry now encompasses a large
variety of application domains, hardware setup types, and processing workflows
designed for different purposes, and spans a range from qualitative defect
inspection of large vehicles to precision measurements of microscopic optics.
Over these years, many exciting developments have accumulated in the underlying
theory, in the systems design, and in the implementation specifics. This
diversity of topics is difficult to grasp for experts and non-experts alike and
may present an obstacle to a wider acceptance of deflectometry as a useful tool
in other research fields and in the industry.
  This paper presents an attempt to summarize the status of deflectometry, and
to map relations between its notable "spin-off" branches. The intention of the
paper is to provide a common communication basis for practitioners and at the
same time to offer a convenient entry point for those interested in learning
and using the method. The list of references is extensive but definitely not
exhaustive, introducing some prominent trends and established research groups
in order to facilitate further self-directed exploration by the reader.

Optics;Computer Vision and Pattern Recognition;Instrumentation and Detectors