On applications of hypergeometric functions

This is a survey article on the authorʹs involvement over the years with hypergeometric functions. We discuss our counter-example to one of M. Robertsonʹs conjectures, our results on the omitted values problems, Brannanʹs conjecture on the coefficients of a certain power series, generalizations of Ramanujanʹs asymptotic formulas for complete elliptic integrals and Muirʹs 1883 approximation to the arc length of an ellipse involving an inequality for some 3F2ʹs.