Fluorescence lifetime sensing enables researchers to probe the physicochemical environment of a fluorophore providing a window through which we can observe the complex molecular make-up of the cell. Fluorescence lifetime imaging microscopy (FLIM) quantifies and maps cell biochemistry, a complex ensemble of dynamic processes. Unfortunately, typical high-resolution FLIM systems exhibit rather limited acquisition speeds, often insufficient to capture the time evolution of biochemical processes in living cells. Here, we describe the theoretical background that justifies the developments of high-speed single photon counting systems. We show that systems with low dead-times not only result in faster acquisition throughputs but also improved dynamic range and spatial resolution. We also share the implementation of hardware and software as an open platform, show applications of fast FLIM biochemical imaging on living cells and discuss strategies to balance precision and accuracy in FLIM. The recent innovations and commercialisation of fast time-domain FLIM systems are likely to popularise FLIM within the biomedical community, to impact biomedical research positively and to foster the adoption of other FLIM techniques as well. While supporting and indeed pursuing these developments, with this work we also aim to warn the community about the possible shortcomings of fast single photon counting techniques and to highlight strategies to acquire data of high quality.