Kepler and K2 have enabled studies of exoplanets and stars. This thesis focuses on two goals: characterising starspots on Kepler stars and finding and following up K2 exoplanets.Starspot evolution produces quasi-sinusoidal light curves. Fitting ACFs with periodic functions, I found a correlation between starspot size, decay lifetime and stellar effective temperature. This method is used as part of RV follow-up for planet-hosting stars. K2 light curves were analysed using a new pipeline. This generated two confirmed planets: K2-140b, a Jupiter-like planet orbiting in 6.57 days (the 9th hot Jupiter from K2) and K2-311b, a single-transit-event lasting 54 hours. With RV follow-up and tools, this Jupiter-sized planet orbits in 10 years. This is currently the longest-period transiting planet discovered. This thesis contributes to future exoplanet endeavours to discover smaller planets in distant orbits, by providing techniques for exoplanet follow-up and improving our knowledge and understanding of stellar activity.