Qualityadjusted life year (QALY) models are widely used for economic evaluation in the health care sector. In the first part of the paper, we establish an overview of QALY models where health varies over time and provide a theoretical analysis of model identification and parameter estimation from time tradeoff (TTO) and standard gamble (SG) scores. We investigate deterministic and probabilistic models and consider five different families of discounting functions in all. The second part of the paper discusses four issues recurrently debated in the literature. This discussion includes questioning the SG method as the gold standard for estimation of the health state index, reexamining the role of the constantproportional tradeoff condition, revisiting the problem of double discounting of QALYs, and suggesting that it is not a matter of choosing between TTO and SG procedures as the combination of these two can be used to disentangle risk aversion from discounting. We find that caution must be taken when drawing conclusions from models with chronic health states to situations where health varies over time. One notable difference is that in the former case, risk aversion may be indistinguishable from discounting