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The two-dimensional material graphene possesses many impressive properties such asextraordinary carrier mobility, mechanical stiffness and optical transmittance. However,the properties of pristine graphene do not always complement the requirements of applications. Of particular interest, a band gap is needed for electronic logic devices. Recent research shows that using few-layer hexagonal boron nitride as a substrate for graphene-based electronic devices can open a band gap in graphene. Also, introducing impurities such as hydrogen atoms, transition metals or silicon atoms on or within graphene can control the electronic properties according to recent studies. Furthermore, ion irradiation is an alternative option to tailor the properties of graphene by introducing defects. In this thesis, pristine, impure or defective graphene and few-layer boron nitride were characterised by scanning transmission electron microscopy (STEM) and electron energy loss (EEL) spectroscopy. Through STEM and EEL spectroscopy, lattice structures and electronic properties of these two-dimensional materials could be investigated at the atomic scale. This thesis focuses on the frontier studies of theoretical and experimental EEL spectroscopy of graphene and few-layer boron nitride with impurities. In the EEL spectra of pristine graphene and boron nitride two prominent peaks were observed, which are attributed to the plasmon excitations of π- and π+σ-electrons. By introducing impurities such as hydrogen adatoms on graphene and substitutional oxygen and carbon atoms within single-layer boron nitride, our experimental and simulated EEL spectra show that their π-plasmon peaks are modified. The concentrations of these impurities were then evaluated via EEL spectra and atomic-resolution images. If other impurities, such as various transition metals and silicon atoms, are introduced on or within single-layer graphene, our simulated EEL spectra demonstrate that the geometry of these impurity clusters affects the π-plasmon peak in graphene and some impurities even enhance it. Finally, experiments on in-situ transmission electron microscopy and ex-situ STEM and Raman spectroscopy were conducted to investigate ion irradiated graphene. Many topological defects were, for the first time, observed in atomic-resolution STEM images of ion irradiated graphene. Simulated EEL spectra of defective graphene are also reported, which suggests that corrugations and dangling bonds in defects can modify out-of-plane EEL spectra and introduce intraband transitions, respectively.