  In this paper, we overview the recent progresses on the lifespan estimates of
classical solutions of the initial value problems for nonlinear wave equations
in one space dimension. There are mainly two directions of the developments on
the model equations which ensure the optimality of the general theory. One is
on the so-called "combined effect" of two kinds of the different nonlinear
terms, which shows the possibility to improve the general theory. Another is on
the extension to the non-autonomous nonlinear terms which includes the
application to nonlinear damped wave equations with the time-dependent critical
case.
