Sleep is characterized by an intricate variation of brain activity over time. Measuring these temporal sleep dynamics is relevant for elucidating healthy and pathological sleep mechanisms. The rapidly increasing possibilities for obtaining and processing sleep registrations have led to an abundance of data, which can be challenging to analyze and interpret. This review provides a structured overview of approaches to represent temporal sleep dynamics, categorized based on the way the source data is compressed. For each category of representations, we describe advantages and disadvantages. Standard human-defined 30-s sleep stages have the advantages of standardization and interpretability. Alternative human-defined representations are less standardized but offer a higher temporal resolution (in case of microstructural events such as sleep spindles), or reflect non-categorical information (for example spectral power analysis). Machine-learned representations offer additional possibilities: automated sleep stages are useful for handling large quantities of data, while alternative sleep stages obtained from clustering data-driven features could aid finding new patterns and new possible clinical interpretations. While newly developed sleep representations may offer relevant insights, they can be difficult to interpret in for example a clinical context. Therefore, there should always be a balance between developing these sophisticated sleep analysis techniques and maintaining clinical explainability.