The stylistic properties of text have intrigued computational linguistics researchers in recent years. Specifically, researchers have investigated the Text Style Transfer (TST) task, which aims to change the stylistic properties of the text while retaining its style independent content. Over the last few years, many novel TST algorithms have been developed, while the industry has leveraged these algorithms to enable exciting TST applications. The field of TST research has burgeoned because of this symbiosis. This article aims to provide a comprehensive review of recent research efforts on text style transfer. More concretely, we create a taxonomy to organize the TST models and provide a comprehensive summary of the state of the art. We review the existing evaluation methodologies for TST tasks and conduct a large-scale reproducibility study where we experimentally benchmark 19 state-of-the-art TST algorithms on two publicly available datasets. Finally, we expand on current trends and provide new perspectives on the new and exciting developments in the TST field.