The relationship between stimuli and the BOLD response they elicit is often modeled using a linear time invariant (LTI) system, where a time series of hypothesized metabolic activity is the input and an estimated or assumed hemodynamic response function (HRF) is the impulse response function. This talk focuses on situations when the exact form of the stimulus or HRF is not known a priori. We begin by discussing a variety of linear and non-linear techniques for estimating the HRF. For each method, we introduce techniques for estimating amplitude, peak latency, and duration and for performing inference in a multi-subject fMRI setting. We then assess each technique's relative sensitivity and its propensity for mis-attributing task effects on one parameter (e.g., duration) to another (e.g., amplitude). Finally, we introduce methods for quantifying model misspecification and assessing the bias and power-loss related to the choice of model. Overall, the results show that it is surprisingly difficult to accurately recover true task-evoked changes in BOLD signal, and that there are substantial differences among models in terms of power, bias and parameter confusability. Finally, we discuss situations when the stimulus onset and duration are unknown. In these situations change point methods can be used to make inferences about activation. In this talk I will discuss methods for estimating an unknown distribution of onset times and durations using these methods.