Just-in-time (JIT) compilers are key components for many popular programming languages with managed runtimes (e.g., Java and JavaScript). JIT compilers perform optimizations and generate native code at runtime based on dynamic profiling data, to improve the execution performance of the running application. Like other software systems, JIT compilers might have software bugs, and prior work has developed a number of automated techniques for detecting functional bugs (i.e., generated native code does not semantically match that of the original code). However, no prior work has targeted JIT compiler performance bugs, which can cause significant performance degradation while an application is running. These performance bugs are challenging to detect due to the complexity and dynamic nature of JIT compilers. In this paper, we present the first work on demystifying JIT performance bugs. First, we perform an empirical study across four popular JIT compilers for Java and JavaScript. Our manual analysis of 191 bug reports uncovers common triggers of performance bugs, patterns in which these bugs manifest, and their root causes. Second, informed by these insights, we propose layered differential performance testing, a lightweight technique to automatically detect JIT compiler performance bugs, and implement it in a tool called Jittery. We incorporate practical optimizations into Jittery such as test prioritization, which reduces testing time by 92.40% without compromising bug-detection capability, and automatic filtering of false-positives and duplicates, which substantially reduces manual inspection effort. Using Jittery, we discovered 12 previously unknown performance bugs in the Oracle HotSpot and Graal JIT compilers, with 11 confirmed and 6 fixed by developers.