To avoid software vulnerabilities, organizations are shifting security to earlier stages of the software development, such as at code review time. In this paper, we aim to understand the developers' perspective on assessing software security during code review, the challenges they encounter, and the support that companies and projects provide. To this end, we conduct a two-step investigation: we interview 10 professional developers and survey 182 practitioners about software security assessment during code review. The outcome is an overview of how developers perceive software security during code review and a set of identified challenges. Our study revealed that most developers do not immediately report to focus on security issues during code review. Only after being asked about software security, developers state to always consider it during review and acknowledge its importance. Most companies do not provide security training, yet expect developers to still ensure security during reviews. Accordingly, developers report the lack of training and security knowledge as the main challenges they face when checking for security issues. In addition, they have challenges with third-party libraries and to identify interactions between parts of code that could have security implications. Moreover, security may be disregarded during reviews due to developers' assumptions about the security dynamic of the application they develop. Data and materials: https://doi.org/10.5281/zenodo.6875435