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The magnetic fields that thread extragalactic radio jets play an important role in the emission properties and evolution of these objects; knowledge of the structure and evolution of these magnetic fields is therefore important in forming a better understanding of jets by imposing constraints on theoretical models and simulations. This thesis presents a method to infer the geometry of the magnetic fields that thread jets by comparing the transverse (across the jet) emission properties of jets with predictions from models. Such comparisons are possible thanks to the high resolution radio images of jets produced using the technique of VLBI polarimetry, which allows forjets to be sufficiently resolved across their length. The radio images presented in this work reveal several features in the transverse structure of jets: i) the total and polarized intensity can be asymmetrically distributed across the jet, ii) the total and polarized intensity maxima can be significantly displaced with respect to each other, iii) total and polarized intensity may be edge brightened and iv) the apparent magnetic field may flip by an angle of 90° across the jet. All four features can be successfully explained by assuming that jets are threaded by magnetic fields of helical geometry. Models already proposed in the literature (examined by Laing 1981) are tested against observations and enhanced accordingly in order to account for any discrepancies with observations. These enhancements include the addition of a tangled magnetic field component and radial compression at the outer sheath of a jet. Comparisons with observations reveal that a helical magnetic field geometry of constant pitch angle combined with a tangled magnetic field component (to adjust the fractional polarization) can successfully predict the structure of the inner jet but fail at the edges where the predicted fractional polarization is lower than that observed; the radial compression is introduced in order to account for this discrepancy but despite this having the desired effect, predicted fractional polarization still falls short of the observed values. Comparisons with other geometries discussed by Laing (Chan-Henricksen, hollow jet) produced unsatisfactory results. One of the predictions of the helical magnetic field model is that the projected magnetic field can have one of four different behaviours, two of which are commonly observed (magnetic field across the jet being either parallel or perpendicular to the jet ridge line) and two less commonly (magnetic field across the jet abruptly changing from parallel to perpendicular and magnetic field being parallel at the edges and perpendicular at the middle). The two common behaviours have been associated with quasars (parallel field) and BL Lac objects (perpendicular field) (Cawthorne et al. 1993a, 1993b). A simple statistical model that predicts the likelihood of observation of these behaviours has been developed and is presented in this thesis. The results from the model show that the all parallel magnetic field behaviour (quasar type) is the most common while perpendicular magnetic fields can account for a small fraction (- 10 percent) of the observations. The model also suggests that the two uncommon behaviours should be more likely to be observed in high flux sources.