A survey of the literature is presented on various statistical inference problems and procedures associated with the following experimental setting: Any level of dose of some treatmenc can be administered to each ekperimental unit, and the observed response on each unit is binary ("success" or "failure") with the unknown success probability being a nondecreasing function of the dose-level. This function is referred to as a quantal response curve. Both parametric and nonparametrie models for a quantal response curve are considered. In each case both single-stage and sequential estimation procedures are reviewed in detail. This survey was motivated by the following statistical selection problem: Suppose that there are available several treatments, and that each one has associated with it a completely unknown quantal response curve. For each curve define its qth quantile (EDlOOq) as the dose-level which corresponds to a "success" probability of q where qe (0,1) is specified. For any prespecified q we wish to select the treatment associated with the smallest EDlOOq. Some difficulties inherent in solving this selection problem, and possible approaches to devising statistical procedures for achieving the stated goal are discussed. We have not found satisfactory solutions to these difficulties, and the problem is essentially open.