The distribution of values of $L$-functions in the critical strip and applications

In this talk, I will survey the history of the value distribution
theory of $L$-functions in the critical strip, focusing in particular on what is
known at the right of the critical line. I will then give three main applications
of this theory: counting zeros of linear combinations of $L$-functions near the
critical line, studying the distribution of class numbers of various families of
quadratic fields, and counting sign changes of quadratic character sums and
real zeros of Fekete polynomials.