Interaction testing can be used to effectively detect faults that are otherwise difficult to find by other testing techniques. However, in practice, the input configurations of software systems are subjected to constraints, especially in the case of highly configurable systems. Handling constraints effectively and efficiently in combinatorial interaction testing is a challenging problem. Nevertheless, researchers have attacked this challenge through different techniques, and much progress has been achieved in the past decade. Thus, it is useful to reflect on the current achievements and shortcomings and to identify potential areas of improvements. This paper presents the first comprehensive and systematic literature study to structure and categorize the research contributions for constrained interaction testing. Following the guidelines of conducting a literature study, the relevant data are extracted from a set of 103 research papers belonging to constrained interaction testing. The topics addressed in constrained interaction testing research are classified into four categories of constraint test generation, application, generation and application, and model validation studies. The papers within each of these categories are extensively reviewed. Apart from answering several other research questions, this paper also discusses the applications of constrained interaction testing in several domains, such as software product lines, fault detection and characterization, test selection, security, and graphical user interface testing. This paper ends with a discussion of limitations, challenges, and future work in the area.