Multivariate analysis is an important kind of method in process monitoring and fault detection, in which the canonical correlation analysis (CCA) makes use of the correlation change between two groups of variables to distinguish the system status and has been greatly studied and applied. For the monitoring of nonlinear dynamic systems, the deep neural network-aided CCA (DNN-CCA) has received much attention recently, but it lacks a general definition and comparative study of different network structures. Therefore, this article first introduces four deep neural network (DNN) models that are suitable to combine with CCA, and the general form of DNN-CCA is given in detail. Then, the experimental comparison of these methods is conducted through three cases, so as to analyze the characteristics and distinctions of CCA aided by each DNN model. Finally, some suggestions on method selection are summarized, and the existed open issues in the current DNN-CCA form and future directions are discussed.