Personal data collected at scale promises to improve decision-making and accelerate innovation. However, sharing and using such data raises serious privacy concerns. A promising solution is to produce synthetic data, artificial records to share instead of real data. Since synthetic records are not linked to real persons, this intuitively prevents classical re-identification attacks. However, this is insufficient to protect privacy. We here present PrivE, a toolbox of attacks to evaluate synthetic data privacy under a wide range of scenarios. These attacks include generalizations of prior works and novel attacks. We also introduce a general framework for reasoning about privacy threats to synthetic data and showcase PrivE on several examples.