This paper summarizes the results of an intercomparison on the use of the ICRP Reference Computational Phantoms with radiation transport codes, which was organized by EURADOS working group 6. Three exercises are described: exposure to an anterior-posterior (AP) photon point source, exposure to an AP neutron point source, and exposure to two typical medical X-ray examinations. The three exercises received 17, 8 and 8 solutions, respectively. Participants originated from fifteen different countries, and used a wide range of Monte Carlo codes. Due to difficulties in defining the precise source location unambiguously in the exercise description, agreement to within ∼10% of the reference solution was considered satisfactory for a given participant's results. Although some participants provided initial solutions in good agreement with the reference solutions, differences of several tens of percent, or even several orders of magnitude, were exhibited for many of the others. Following feedback and suggestions from the organizers, revised solutions were submitted by some of the participants for the photon exercises; in general, agreement was improved. The overall observations from these three intercomparison exercises are summarized and discussed.