A classification and characterization is given of the more important transport phenomena in macroporous media (molecular diffusion, viscous flow, transport phenomena involving moving menisci: wetting, capillary rise, drainage, drying). Pore space models are used to obtain values for the transport coefficient (effective diffusion coefficient, permeability) and — when applicable — the driving force (capillary potential) in the transport equation. These models and this approach have to be distinguished from (i) models used in simulating particle packings, (ii) models used in determining the so-called pore size distribution (suction technique, mercury porosimetry), (iii) analytic calculation of the transport coefficient, and (iv) overall description of the transport phenomena (in which the microscopic pore space structure is not accounted for). An enumeration of almost all proposed pore space models is presented and classified with reference to the pore space interconnectivity. This interconnectivity may be one-dimensional (tubes in parallel, in series; tubes with constrictions; random adjacent slices models), two-dimensional (network models), three-dimensional (regular sphere packings; tetrahedra networks; tubes and/or junctions randomly in space), and strictly zero-dimensional (simple capillary elements used in ad hoc explanations; independent domain theory). In order to remove too optimistic ideas about the use of pore space models, all models are checked against the phenomena of capillary rise ( e.g. water in sand). The predictions of the models regarding statics and dynamics of capillary rise are compared with the experimental facts and it appears that none of the models can give even a qualitative description of the observed phenomena. The situation is not as bad for other transport phenomena as it is for capillary rise, but it should be realized that even slightly different transport phenomena require a different approach and, further, that improvement of pore space models should be directed by a more careful analysis of the non-macroscopic physical phenomena. It is the ghost of the concept of a pore size (distribution) that plays a dominant role here. This concept is analysed. Finally, a number of seemingly comparable phenomena or concepts are discussed: drainage — imbibition; suction — mercury porosimetry; molecular diffusion — viscous flow; capillary potential and permeability as a function of liquid content. Tacitly this comparison gives an evaluation of the pore space models for the transport phenomena involved. Suggestions for further research are given.