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The transit method is the most successful tool for exoplanet discovery to date. With more than half of all known exoplanets discovered by \emph{Kepler} using this method, the mission also revealed a number of objects with dimming events that defy the common explanations, the most prominent being KIC 8462852 aka ``Tabby's star''. I embarked on a search for objects with such irregular transit signatures in the data of K2, the two-wheeled successor mission of \emph{Kepler}. My method is a combination of automated pre-selection of targets showing downward flux excursions and visual light curve inspection of the selected subset comprising about \SI{1.5}{\percent} of the initial sample. In addition, I developed a tool to constrain the effective temperature of a planet-hosting star from photometry alone. This software finds broad application in any science case where a photometric spectral type estimate is necessary. I used existing transit models and Bayesian inference to perform a Markov Chain Monte Carlo (MCMC) analysis of a planetary candidate I discovered. This putative gas giant is in a \SI{1.32}{\day} circular orbit with an exceptionally tight orbital radius of $a \approx 0.012\,\mathrm{AU}$. My analysis revealed a scaled planetary radius of $R_\mathrm{p}/R_\star = 0.0927\pm0.0026$ and an edge-on orientation with an inclination $i=89.8\substack{+3.0 \\ -3.4}$. EPIC 217393088.01 is one of the closest-orbiting exoplanets ever detected and the first giant planet with such a small orbital radius. An additional major finding of my search is EPIC 220262993, which exhibits aperiodic, asymmetric dips in flux with rapid dimming rates and up to \SI{\sim 25}{\percent} depth, lasting for \SIrange{2}{4}{\day}. In previous works based on optical and mid-infrared photometry, this object was inconsistently classified as a possible quasar or a white dwarf. We conducted follow-up observations both photometrically with GROND on the MPI/ESO \SI{2.2}{\meter} telescope in La Silla (Chile) and spectroscopically with FIRE on the Magellan/Baade \SI{6.5}{\meter} telescope. With additional spectroscopy using ESI on the Keck \rom{2} \SI{10}{\meter} telescope we were able to distinguish between these cases: EPIC 220262993 is a quasar with redshift $z=1.42$. This is the only known exemplar showing deep dips in flux on such a short time scale.