  A Bernstein-von Mises theorem is derived for general semiparametric
functionals. The result is applied to a variety of semiparametric problems in
i.i.d. and non-i.i.d. situations. In particular, new tools are developed to
handle semiparametric bias, in particular for nonlinear functionals and in
cases where regularity is possibly low. Examples include the squared $L^2$-norm
in Gaussian white noise, nonlinear functionals in density estimation, as well
as functionals in autoregressive models. For density estimation, a systematic
study of BvM results for two important classes of priors is provided, namely
random histograms and Gaussian process priors.
