Many of the technological advances we witness today are based on novel and innovative ways to derive value from data sets. However, these data sets are often comprised of personal or confidential data records which prohibits or complicates their direct use. In the complex contemporary data processing pipelines that drive many applications, synthetic data sets can be used as surrogate replacements of original data, and this --at least at face value-- alleviates these concerns. However, evaluating the privacy and confidentiality of synthetic data is not straightforward. While much attention is spent on metrics and quantification approaches, a broader threat model-oriented perspective is lacking. In this literature review article, we provide overview of the different approaches, metrics, assumptions and attacker models used in academic research to evaluate the privacy of tabular synthetic data. This study shows that scientific privacy evaluations in this domain is increasingly diverse and diverging, with different studies adopting different privacy threat models, under different attacker assumptions and different privacy metrics --- both non-adversarial and adversarial. Based on our findings, we argue in favor of more harmonized and concerted efforts within the broader research domain, to promote more complete and empirically sound benchmarks and evaluations of privacy risks in the use of synthetic data.