Advances in neural signal and image acquisition as well as in multivariate signal processing and machine learning are enabling a richer and more rigorous understanding of the neural basis of human decision-making. Decision-making is essentially characterized behaviorally by the variability of the decision across individual trials--e.g., error and response time distributions. To infer the neural processes that govern decision-making requires identifying neural correlates of such trial-to-trial behavioral variability. In this paper, we review efforts that utilize signal processing and machine learning to enable single-trial analysis of neural signals acquired while subjects perform simple decision-making tasks. Our focus is on neuroimaging data collected noninvasively via electroencephalograpy (EEG) and functional magnetic resonance imaging (fMRI). We review the specific framework for extracting decision-relevant neural components from the neuroimaging data, the goal being to analyze the trial-to-trial variability of the neural signal along these component directions and to relate them to elements of the decision-making process. We review results for perceptual decision-making and discrimination tasks, including paradigms in which EEG variability is used to inform an fMRI analysis. We discuss how single-trial analysis reveals aspects of the underlying decision-making networks that are unobservable using traditional trial-averaging methods.