In the era of the internet of things (IoT), software-enabled inter-connected devices are of paramount importance. The embedded systems are very frequently used in both security and privacy-sensitive applications. However, the underlying software (a.k.a. firmware) very often suffers from a wide range of security vulnerabilities, mainly due to their outdated systems or reusing existing vulnerable libraries; which is evident by the surprising rise in the number of attacks against embedded systems. Therefore, to protect those embedded systems, detecting the presence of vulnerabilities in the large pool of embedded devices and their firmware plays a vital role. To this end, there exist several approaches to identify and trigger potential vulnerabilities within deployed embedded systems firmware. In this survey, we provide a comprehensive review of the state-of-the-art proposals, which detect vulnerabilities in embedded systems and firmware images by employing various analysis techniques, including static analysis, dynamic analysis, symbolic execution, and hybrid approaches. Furthermore, we perform both quantitative and qualitative comparisons among the surveyed approaches. Moreover, we devise taxonomies based on the applications of those approaches, the features used in the literature, and the type of the analysis. Finally, we identify the unresolved challenges and discuss possible future directions in this field of research.