To protect cryptographic implementations from side-channel vulnerabilities, developers must adopt constant-time programming practices. As these can be error-prone, many side-channel detection tools have been proposed. Despite this, such vulnerabilities are still manually found in cryptographic libraries. While a recent paper by Jancar et al. shows that developers rarely perform side-channel detection, it is unclear if existing detection tools could have found these vulnerabilities in the first place. To answer this question we surveyed the literature to build a classification of 34 side-channel detection frameworks. The classification we offer compares multiple criteria, including the methods used, the scalability of the analysis or the threat model considered. We then built a unified common benchmark of representative cryptographic operations on a selection of 5 promising detection tools. This benchmark allows us to better compare the capabilities of each tool, and the scalability of their analysis. Additionally, we offer a classification of recently published side-channel vulnerabilities. We then test each of the selected tools on benchmarks reproducing a subset of these vulnerabilities as well as the context in which they appear. We find that existing tools can struggle to find vulnerabilities for a variety of reasons, mainly the lack of support for SIMD instructions, implicit flows, and internal secret generation. Based on our findings, we develop a set of recommendations for the research community and cryptographic library developers, with the goal to improve the effectiveness of side-channel detection tools.