Bayesian Optimal Interval (BOIN) designs are a class of model-assisted dose-finding designs that can be used in oncology trials to determine the maximum tolerated dose (MTD) of a study drug based on safety or the optimal biological dose (OBD) based on safety and efficacy. BOIN designs provide a complete suite for dose finding in early phase trials, as well as a consistent way to explore different scenarios such as toxicity, efficacy, continuous outcomes, delayed toxicity or efficacy and drug combinations in a unified manner with easy access to software to implement most of these designs. Although built upon Bayesian probability models, BOIN designs are operationally simple in general and have good statistical operating characteristics compared to other dose-finding designs. This review paper describes the original BOIN design and its many extensions, their advantages and limitations, the software used to implement them, and the most suitable situation for use of each of these designs. Published examples of the implementation of BOIN designs are provided in the Appendix.