  We give an overview of basic methods that can be used for obtaining
asymptotic expansions of integrals: Watson's lemma, Laplace's method, the
saddle point method, and the method of stationary phase. Certain developments
in the field of asymptotic analysis will be compared with De Bruijn's book {\em
Asymptotic Methods in Analysis}. The classical methods can be modified for
obtaining expansions that hold uniformly with respect to additional parameters.
We give an overview of examples in which special functions, such as the
complementary error function, Airy functions, and Bessel functions, are used as
approximations in uniform asymptotic expansions.
