This book is devoted to (a) multivariate models for non-normal re­ sponse, an area of probability and statistics with increasing activity and applications, and (b) dependence concepts that are useful for analysing properties of multivariate models. It also adds to the knowledge of the space of multivariate distributions. By a multivariate model, I mean a parametric statistical model for a multivariate response, possibly with covariates. Examples are models for multivariate or longitudinal count, binary and ordinal response data. My approach consists of the modelling of the uni­ variate margins followed by adding the appropriate dependence structure, with considerations of positive or negative dependence, and exchangeable, time series or general dependence structure. I find that dependence concepts and dependence analysis are neces­ sary to understand a model and when it might be applicable. This includes analysis of the range of dependence that a model permits and whether the dependence of the model increases as multivariate parameters increase.