This paper discusses some of the recent developments in testing linear
ity of a time series against the alternative that the series has been
generated by a nonlinear process. The focus is on testing linearity ag
ainst parametric alternatives. Special attention is given to the situa
tions in which the parametric nonlinear model only is identified under
the alternative but not under the null hypothesis of linearity. The u
se of some of the linearity tests in the modelling of nonlinear series
is considered and illustrated with an example.