  Copulas have been popular to model dependence for multivariate distributions,
but have not been used much in modelling temporal dependence of univariate time
series. This paper demonstrates some difficulties with using copulas even for
Markov processes: some tractable copulas such as mixtures between copulas of
complete co- and countermonotonicity and independence (Fr\'{e}chet copulas) are
shown to imply quite a restricted type of Markov process and Archimedean
copulas are shown to be incompatible with Markov chains. We also investigate
Markov chains that are spreadable or, equivalently, conditionally i.i.d.
