Poisson models are appropriate when dealing with count data (non-negative integer data), which is usually severely skewed. A consequence of using Poisson distributions (and potentially, a problem) is that the mean and variance of the distribution are governed by the same parameter (lambda). Therefore, in a Poisson model, the residuals should always be checked, and special care needs to be taken with the variance/mean of them. If the variance is increasing as the mean increases, we should adjust our model and use the negative binomial distribution, which is a generalization of the Poisson distribution with an extra parameter to control the variance. 

On a conceptual level, all the regular lmer/lme4 functions that can be used for linear models can also be applied here for GLMs.