The Behrens-Fisher problem arises when one seeks to make inferences about the means of two normal populations without assuming the variances are equal. This paper presents a review of fundamental concepts and applications used to address the Behrens-Fisher problem under fiducial, Bayesian, and frequentist approaches. Methods of approximations to the Behrens-Fisher distribution and a simple Bayesian framework for hypothesis testing are also discussed. Finally, a discussion is provided for the use of generalized "p" values in significance testing of hypotheses in the presence of nuisance parameters. It is shown that the generalized "p" value based on a frequentist probability for the Behrens-Fisher problem is numerically the same as those from the fiducial and Bayesian solutions. A table of tests of significance is also included. (Contains 3 tables, 2 figures, and 93 references.) (Author)