The transport of proteins and lipids is one of the main cellular functions. The vesicular model, compartment (or cisterna) maturation model, and the diffusion model compete with each other for the right to be the paradigm within the field of the intra-Golgi transport. These models have significant difficulties explaining the existing experimental data. Recently, we proposed the kiss-and-run (KAR) model of intra-Golgi transport (Mironov and Beznoussenko in Int J Mol Sci 13(6):6800-6819, 2012), which can be symmetric, when fusion and fission occur in the same location, and asymmetric, when fusion and fission take place at different sites. Here, we compare the ability of main models of the intra-Golgi transport to explain the existing results examining the evidence in favor and against each model. We propose that the KAR model has the highest potential for the explanation of the majority of experimental observations existing within the field of intracellular transport.