Patients follow-up in oncology is generally performed through the acquisition of dynamic sequences of contrast-enhanced images. Estimating parameters of appropriate models of contrast intake diffusion through tissues should help characterizing the tumour physiology. However, several models have been developed and no consensus exists on their clinical use. In this paper, we propose a unified framework to analyse models of perfusion and estimate their parameters in order to obtain reliable and relevant parametric images. After defining the biological context and the general form of perfusion models, we propose a methodological framework for model assessment in the context of parameter estimation from dynamic imaging data: global sensitivity analysis, structural and practical identifiability analysis, parameter estimation and model comparison. Then, we apply our methodology to five of the most widely used compartment models (Tofts model, extended Tofts model, two-compartment model, tissue-homogeneity model and distributed-parameters model) and illustrate the results by analysing the behaviour of these models when applied to data acquired on five patients with abdominal tumours.