This thesis aims to understand more about the developmental histories of galaxies and their internal components by studying the wavelength dependence of their spatial structure. I use a large sample of low-redshift galaxies with optical–near-IR imaging from the GAMA survey, which have been fitted with Sérsic and Sérsic + exponential functions in nine wavebands simultaneously, using software developed by the MegaMorph project. The first section of this thesis examines how the sizes and radial profiles of galaxies vary with wavelength. To quantify the wavelength dependence of effective radius I use the ratio, R, of measurements in two restframe bands. The dependence of Sérsic index on wavelength, N, is computed correspondingly. I show that accounting for different redshift and luminosity selections partly reconciles variations between several recent studies. Dividing galaxies by visual morphology confirms the behaviour inferred using morphological proxies, although our quantitative measurements allow me to study larger and fainter samples. I then demonstrate that varying dust opacity and disc inclination can account for features of the joint distribution of R and N for late-type galaxies. However, dust does not appear to explain the highest values of R and N. The bulge-disc nature of galaxies must also contribute to the wavelength-dependence of their structure. The second section of this thesis studies radial colour gradients across the galaxy population. I use the multi-wavelength information provided by MegaMorph analysis of galaxy light profiles to calculate intrinsic colour gradients, and divide into six subsamples split by overall Sérsic index (n) and galaxy colour. I find a bimodality in the colour gradients of high- and low-n galaxies in all wavebands which varies with overall galaxy luminosity. Global trends in colour gradients therefore result from combining the contrasting behaviour of a number of different galaxy populations. The ubiquity of strong negative colour gradients supports the picture of inside-out growth through gas accretion for blue, low-n galaxies, and through dry minor mergers for red, high-n galaxies. An exception is the blue high-n population which has properties indicative of dissipative major mergers. In the third section of this thesis I apply bulge-disc decompositions to my sample of galaxies, in order to discover the structural origin of the wavelength dependences found in the previous two chapters. I find that most galaxies with a substantial disc, even those with no discernible bulge, display a high value of N. The increase in Sérsic index to longer wavelengths is therefore intrinsic to discs, apparently resulting from radial variations in stellar population and/or dust reddening. Similarly, low values of R (< 1) are found to be ubiquitous, implying an element of universality in galaxy colour gradients. I also study how bulge and disc colour distributions vary with galaxy type. I find that, rather than all bulges being red and all discs being blue in absolute terms, both components become redder for galaxies with redder total colours. I even observe that bulges in bluer galaxies are typically bluer than discs in red galaxies, and that bulges and discs are closer in colour for fainter galaxies. Trends in total colour are therefore not solely due to the colour or flux dominance of the bulge or disc.