For over 35 years, the violation-of-expectation (VOE) paradigm has been used to study the development, during the first three years of life, of a wide range of cognitive expectations, including physical, psychological, biological, sociomoral, numerical, statistical, probabilistic, and linguistic expectations. Surprisingly, despite the paradigm’s widespread use and the many seminal findings it has contributed to psychological science over the years, there has not yet been an attempt at providing a detailed, in-depth analysis of its development and conceptual underpinnings. Here, we attempted to do just that. We first focus on the rationale of the paradigm and discuss how it has evolved over time. Next, we show how a panoply of methodological advances and extensions has helped broaden and strengthen the paradigm. We then turn to a review of the paradigm’s main strengths and limitations. Finally, we end with a discussion of various challenges that have been leveled against the paradigm over the years. Through it all, our goal was two-fold. First, we sought to provide future generations of developmental psychologists and other social scientists with an informed and constructive introduction to the conceptual underpinnings of the VOE paradigm. Second, we wanted to take stock on what the paradigm has revealed to date about how infants form expectations about events, and about how surprise at unexpected events, in or out of the laboratory, can lead to learning, by prompting infants to revise their working model of the world so as to form more accurate expectations in the future.