Measuring biological data across time and space is critical for understanding complex biological processes and for various biosurveillance applications. However, such data are often inaccessible or difficult to directly obtain. Less invasive, more robust and higher-throughput biological recording tools are needed to profile cells and their environments. DNA-based cellular recording is an emerging and powerful framework for tracking intracellular and extracellular biological events over time across living cells and populations. Here, we review and assess DNA recorders that utilize CRISPR nucleases, integrases and base-editing strategies, as well as recombinase and polymerase-based methods. Quantitative characterization, modelling and evaluation of these DNA-recording modalities can guide their design and implementation for specific application areas.