S0 galaxies, otherwise known as lenticular galaxies, are very common throughout the Universe, becoming the most dominant kind of galaxy within large galaxy clusters. Yet despite this, how they came to be remains an unanswered question and an area of highly active research. The aim of this thesis is to determine how S0 galaxies form; in particular, to determine which formation pathways are active along with their relative importance. The extensive, high-resolution observations made by the latest galaxy survey programs, combined with recent advancements in cosmological simulations present an excellent opportunity to explore the formation of S0s in new ways and to develop a far deeper understanding of how they form.Firstly, in order to determine if multiple formation pathways are occurring, I carried out an observational study of S0 galaxies using the SAMI galaxy survey. I found that the range in the structure and kinematics of the S0 population could not be explained using a single formation pathway, finding instead that the more pressure-supported S0 galaxies are consistent with the merger formation process while the more rotationally-supported S0 galaxies are consistent with the faded-spiral pathway. I then followed this up with a study using the IllustrisTNG cosmological simulation, identifying S0 galaxies in a way consistent with the observational study and tracing these galaxies back through time. I confirmed that S0s are indeed forming via two main pathways, with 37 percent forming via a cluster-infall event and 57 percent forming via a merger-driven pathway. In addition, I found an example of an S0 forming from the merger between a compact elliptical galaxy (cE) and a gas-rich satellite.The formation of cE galaxies is also uncertain, with observational differences between cE galaxies in different environments suggesting different formation pathways. Given the apparent link between cE and S0 galaxies as well as the similarity in the uncertainties in how these galaxies form, I therefore looked to apply the same approach to investigate the formation of cE galaxies. I found that 68 percent of cE galaxies form in isolation, with around 52 percent of these falling into group environments and becoming passive. The remaining 32 percent of cE galaxies are forming via the stripping of large disk galaxies, which during this process transition through an S0 phase. Finally, using these identified formation pathways and the locations of the resulting cE galaxies, I was able to reproduce the colour, size and metallicity differences observed between isolated and host- associated cE galaxies. The earlier findings of a cE transforming into an S0, along with the finding that many cE galaxies transition through an S0 phase reveal a surprising link between these two seemingly unrelated galaxy types.