I present the work completed during my time as a PhD student within the Exoplanet Group of the Cavendish Laboratory, University of Cambridge, UK, as a part of the Centre for Doctoral Training in Data-Intensive Sciences. Much of this work has been conducted as a part of the NGTS consortium. I implemented and tested a novel generalisation of the autocorrelation function (the G-ACF), which applies to irregularly sampled data, such as photometric light curves from ground-based telescopes. I demonstrated that this algorithm accurately estimated the standard ACF, even for poorly sampled astrophysical data, and produced accurate rotation periods that agreed with more complex and computationally expensive models. I then applied the G-ACF to almost a million photometric light curves from NGTS, finding 16, 880 periodic variability signals from 829, 481 light curves. I combated the noise and aliasing associated with ground-based photometry to produce a stellar variability sample that rivals those from previous space-based photometric studies. I assessed how these variable objects were distributed within colour-magnitude and colour–period space, highlighting distinct populations of variable objects spanning late-A through to mid-M spectral types and with periods between ∼ 0.1and 130 days. Within colour–period space, I found a bi-modal structure previously observed in Kepler data and find samples of stars on either side of the gap appear to be from similar populations of stars in terms of colour, intrinsic brightness and multiplicity rather than distinct epochs of star formation. Finally, I developed a comprehensive period extraction software package, RoTo, which uses multiple period extraction techniques to produce reliable period estimates from time-series data. I applied RoTo to NGTS observations of the ∼ 500 Myr old open cluster NGC 6633. I conducted a detailed study of the rotational variability of member stars, using a combination of literature and machine-learning methods to produce a robust membership list. I calculated distances and extinction values and produced a rotation period sample for the cluster. I compared the slow-rotator sequence of the cluster in colour–period space to similarly aged clusters. I conducted gyro- and isochrone fits to derive probabilistic age estimates for the cluster from rotation, which agreed with age estimates from other methods. This work is firmly rooted within the principles of Data-Intensive Sciences; I applied performant algorithms to large photometric data sets to produce statistical results with minimal manual input. All of the software developed as a part of this PhD is open-source, and I have released two public Python packages.