How do brain representations of the utility of a hedonic goal guide decisions about whether to pursue it? Our focus here will be on brain mechanisms of reward utility operating at particular decision moments in life. Moments such as when you encounter an image, sound, scent or other cue associated in your past with a particular reward; or perhaps just vividly imagine that cue. Such a cue can often trigger a sudden motivational urge to pursue that goal, and sometimes a decision to do so. In drug addicts trying to quit, a cue for the addicted drug might trigger urges that rise to compulsive levels of intensity, despite prior commitments to abstain, leading to the decision to relapse into taking the drug again. Normal or addicted, the urge and decision may well have been lacking immediately before the cue was encountered. The decision to pursue the cued reward might never have happened if the cue had not been encountered. Why can such cues momentarily dominate decision making? The answer involves brain mesolimbic dopamine mechanisms that amplify the incentive salience of reward cues, selectively elevating decision utility to trigger "wanting" for the goal. We describe affective neuroscience studies of brain limbic generators of "wanting" that shed light on how cues trigger pursuit of their goals, both normally and even under intense conditions of irrational goal pursuit.