Heterogeneous parallel architecture (HPA) are inherently more complicated than their homogeneous counterpart. HPAs allow composition of conventional processors, with specialised processors that target particular types of task. However, this makes mapping and scheduling even more complicated and difficult in parallel applications. Therefore, it is crucial to use a robust modelling approach that can capture all the critical characteristics of the application and facilitate the achieving of optimal mapping. In this study, we perform a concise theoretical analysis as well as a comparison of the existing modelling approaches of parallel applications. The theoretical perspective includes both formal concepts and mathematical definitions based on existing scholarly literature. The important characteristics, success factors and challenges of these modelling approaches have been compared and categorised. The results of the theoretical analysis and comparisons show that the existing modelling approaches still need improvement in parallel application modelling in many aspects such as covered metrics and heterogeneity of processors and networks. Moreover, the results assist us to introduce a new approach, which improves the quality of mapping by taking heterogeneity in action and covering more metrics that help to justify the results in a more accurate way.