Traditionally, a dose–toxicity curve is assumed to be monotonic, with the ultimate goal of finding the maximum tolerated dose (MTD). Whereas model-based designs typically use parametric models to facilitate the exchange of information across dose levels, curve-free designs rely solely on the monotonic assumption to extrapolate data between doses. In the first part of this chapter, we present several curve-free designs for phase I trials that were developed over the past decade to identify the MTD in trials involving one or two agents. In recent years, the search for biologically efficacious doses (BEDs) has become increasingly intriguing. Researchers are seeking the optimal efficacy among tolerated doses. The second part of this chapter presents a curve-free design and a hybrid design for BED-finding trials involving one agent, assuming a monotonic dose–toxicity curve and a unimodal dose–efficacy curve. The last section of the chapter provides examples and demonstrations of our Web-based R packages.