For integer-valued time series or multivariate/longitudinal count data with covariates, the copula approach is a convenient way to combine a multivariate model with a univariate margin that is a count regression model (such as negative binomial). Models developed from copulas can have conditional expectations that can be asymptotically linear or sublinear or flat, and are flexible in the univariate margin. Inference and numerical maximum likelihood are straightforward when the copula has a simple analytic form. A data set from the econometrics literature is used for illustration of copula modeling.