This thesis is comprised of two closely related studies of fullerenes. The first part is an investigation of C60 and C70 nanocrystals using both experimental and simulated electron energy loss (EEL) spectra. Through a detailed comparison of particular features in EEL spectra collected from these materials in a transmission electron microscope, with simulated spectra, it is established that differences in spectra from different materials can be linked to particular aspects of the structural models. For example, in the case of C60 differences in experimental spectra from different samples can be linked to differences in the bond lengths within the molecules of different samples. In the case of C70, it is found that features within the spectrum which have previously been attributed to the ten equatorial atoms do not have this origin in a crystal. The second part is an experimental investigation of endohedral fullerenes Nd@C82 and Sc3N@C80. The effect of temperature on the EEL spectrum is investigated and, in the case of Nd@C82, the effect of the presence of different isomers is also investigated. Spectra are successfully obtained from the encapsulated atoms, and the importance of careful experiments in terms of avoiding contamination is highlighted.