Neural activity cannot be directly observed using fMRI; rather it must be inferred from the haemodynamic responses that neural activity causes. Solving this inverse problem is made possible through the use of forward models, which generate predicted haemodynamic responses given hypothesised underlying neural activity. Commonly-used haemodynamic models were developed to explain data from healthy young participants; however studies of ageing and dementia are increasingly shifting the focus towards elderly populations. We evaluated the validity of a range of haemodynamic models across the healthy adult lifespan: from basis sets for linear convolution models (implemented in the general linear models used to analyse most fMRI studies) to nonlinear fitting of a parameterised haemodynamic response function (HRF) and nonlinear fitting of a biophysical generative model (haemodynamic modelling, HDM). Using an exceptionally large sample of participants, and a sensorimotor task optimized for detecting the shape of the HRF, we first characterised the effects of age on descriptive features of the HRF (e.g., peak amplitude and latency). We then compared these to features from more complex nonlinear models, fit to four regions of interest engaged by the task, namely left auditory cortex, bilateral visual cortex, left (contralateral) motor cortex and right (ipsilateral) motor cortex. Finally, we validated the extent to which parameter estimates from these models have predictive validity, in terms of how well they predict age in cross-validated multiple regression. We conclude that age-related differences in the HRF can be captured effectively by models with three free parameters. Furthermore, we show that biophysical models like the HDM have predictive validity comparable to more common models, while additionally providing insights into underlying mechanisms, which go beyond descriptive features like peak amplitude or latency. Here, the HDM revealed that most of the effects of age on the HRF could be explained by an increased rate of vasoactive signal decay and decreased transit rate of blood, rather than changes in neural activity per se. However, in the absence of other types of neural/haemodynamic data, unique interpretation of HDM parameters is difficult from fMRI data alone, and some brain regions in some tasks (e.g, ipsilateral motor cortex) can show responses that are more difficult to capture using current models.