This thesis is concerned with the physics of extragalactic radio - sources. Radio observations of a given source provide a powerful method with which to make direct measurements of the physical processes occuring within the la~ge-scale radio lobes and hotspots . Multi-frequency observations with up to five frequencies have been made for a number of ~ources using the Cambridge 5-km telescope and the Very Large Array. These data have been used to determine the change in radio spectra across the source . to obtain information about the way in which the electron population has evolved. Combining this with inferred magnetic field directions, the dynamics of seven sources have been examined. Additionally the hotspot advance speeds for a statistically representative sample of sources have -been derived. For 3C234 it was possible to test the assumptions used throughout the analysis. They were found to h6ld good to within the limits of error. The results are best interpreted within the framework of a fluid-dynamical model lobes as have recently been examined in numerical experiments. The general distibution of radiating plasma can be understood in terms of the flow of material out of the main accelerating regions (the hotspots - a basic beam model � is assumed thr6ughout) and its subsequent interaction with the surrounding medium, coupled with some precession of the radio jet. As well as looking at source dynamics , the detailed spectra have been used to search for areas of particle acceleration not associated with hotspots. Three sources have been found to have such regions, but large scale acceleration within the radio-lobes is not required . The derivation of ho tspot advance speed for a statistically representative sample has enabled statistical correlations to be investigated . Advance speed is found to be strongly correlated with power and this is discussed in the wider context of overall source models .