In this review, we discuss methods and advancements in fluorescence lifetime imaging microscopy that permit measurements to be performed at faster speed and higher resolution than previously possible. We review fast single-photon timing technologies and the use of parallelized detection schemes to enable high-throughput and high content imaging applications. We appraise different technological implementations of fluorescence lifetime imaging, primarily in the time-domain. We also review combinations of fluorescence lifetime with other imaging modalities to capture multi-dimensional and correlative information from a single sample. Throughout the review, we focus on applications in biomedical research. We conclude with a critical outlook on current challenges and future opportunities in this rapidly developing field.