Phase 1 oncology dose-finding trials are operated under a set of distinct cohorts of patients with a predefined observation period for tracking the binary toxicity outcomes based on defined dose limiting toxicities (DLT). At each moments of decision making, one of three actions (escalate, deescalate, stay at the current dose) is taken based on observed DLTs. Due to randomness of the observed data and small sample sizes of these trials, it is highly desirable to minimize the decision errors of the action taken for next cohort of patients and the BOIN design targets that goal. The optimal interval considers point or composite hypotheses for each action and priors for each of the hypotheses with some specific interest. The dose assignment rule is based on the point estimate of observed DLT rate and posterior probability of one hypothesis is more likely than the other. The entire dose finding procedure of BOIN design is model-free and has good finite and large sample properties for both single and dual agents setting. Additionally, BOIN is more intuitive and transparent, simpler to implement, and yields competitive performance compared to other widely used dose-finding designs.