Humans have the metacognitive ability to assess the accuracy of their decisions via confidence judgments. Many models of the computational mechanisms behind confidence have been developed but there has been little effort to directly compare these models, making it difficult to adjudicate between them. Here, we compare twelve popular process models of confidence by fitting them to large datasets from two experiments in which subjects completed a perceptual task with confidence ratings. The best fitting model was the recently developed lognormal meta noise model, which postulates that confidence is selectively corrupted by signal-dependent noise. Our results cast doubt over popular notions that confidence is derived from post-decisional evidence, from absolute neglect of decision-incongruent evidence, from posterior probability computations, or from a separate decision-making system for metacognitive judgements. Parameter and model recovery analyses showed mostly good recoverability in existing models but with several important exceptions which carry implications for our ability to discriminate between these models. Finally, we evaluated each model’s ability to predict different patterns in the data, which led to additional insight into the workings of individual models. These results present a comprehensive picture of the ability of current confidence models to fit empirical data and suggest that the recently developed lognormal meta noise model is the most likely generative model among current alternatives.