In this thesis, we focus on studies of variable stars across four years of data from NASA's Kepler mission. We present an analysis of oscillating red giants from which exhibit anomalous peaks in their amplitude spectra. We use close analysis of Kepler pixel data to confirm the source of these anomalous peaks. By analysing the distribution of the population across the Kepler field of view, we find that we are observing two populations, of contamination by a line-of-sight background or foreground binary system, and of physical associations in potential triple systems. Using similar population analysis techniques, we study the distribution of Kepler Objects of Interest to draw conclusions about their designation as either planet hosts or false positives. We use detailed pixel analysis methods to study a rotating subgiant hosting a planet, potential doubly-oscillating red giant-delta Scuti binaries, red giants classified by a neural network. We also extend this work to TESS data, to study a sample of high frequency delta Scuti stars. Finally, we perform image subtraction photometry on the Kepler superstamps, large-scale pixel data covering the open clusters NGC 6791 and NGC 6819. Image subtraction photometry produces high-quality time series data which emphasises stellar variability. We outline the development of an image subtraction photometry pipeline, and present an overview of the results of our search for stellar variability in NGC 6791 and NGC 6819, including detections of stellar rotation, binary systems, and oscillating stars in both clusters
