  Implicit copulas are the most common copula choice for modeling dependence in
high dimensions. This broad class of copulas is introduced and surveyed,
including elliptical copulas, skew $t$ copulas, factor copulas, time series
copulas and regression copulas. The common auxiliary representation of implicit
copulas is outlined, and how this makes them both scalable and tractable for
statistical modeling. Issues such as parameter identification, extended
likelihoods for discrete or mixed data, parsimony in high dimensions, and
simulation from the copula model are considered. Bayesian approaches to
estimate the copula parameters, and predict from an implicit copula model, are
outlined. Particular attention is given to implicit copula processes
constructed from time series and regression models, which is at the forefront
of current research. Two econometric applications -- one from macroeconomic
time series and the other from financial asset pricing -- illustrate the
advantages of implicit copula models.
