The tools for spectrally analyzing heart rate variability (HRV) has in recent years grown considerably, with emphasis on the handling of time-varying conditions and confounding factors. Time-frequency analysis holds since long an important position in HRV analysis, however, this technique cannot alone handle a mean heart rate or a respiratory frequency which vary over time. Overlapping frequency bands represents another critical condition which needs to be dealt with to produce accurate spectral measurements. The present survey offers a comprehensive account of techniques designed to handle such conditions and factors by providing a brief description of the main principles of the different methods. Several methods derive from a mathematical/statistical model, suggesting that the model can be used to simulate data used for performance evaluation. The inclusion of a respiratory signal, whether measured or derived, is another feature of many recent methods, e.g., used to guide the decomposition of the HRV signal so that signals related as well as unrelated to respiration can be analyzed. It is concluded that the development of new approaches to handling time-varying scenarios are warranted, as is benchmarking of performance evaluated in technical as well as in physiological/clinical terms.