This dissertation presents novel and practical algorithms to identify the software and hardware components on mobile devices. In particular, we make significant contributions in two challenging areas: library fingerprinting, to identify third-party software libraries, and device fingerprinting, to identify individual hardware components. Our work has significant implications for the privacy and security of mobile platforms. Software-based library fingerprinting can be used to detect vulnerable libraries and uncover large-scale data collection activities. We develop a novel Android library finger-printing tool, LibID, to reliably identify specific versions of in-app third-party libraries. LibID is more effective against code obfuscation than prior art. When comparing LibID with other tools in identifying the correct library version using obfuscated F-Droid apps, LibID achieves an F1 score of more than 0.5 in all cases while prior work is below 0.25. We also demonstrate the utility of LibID by detecting the use of a vulnerable version of the OkHttp library in nearly 10% of the 3 958 popular apps on the Google Play Store. Hardware-based device fingerprinting allows apps and websites to invade user privacy by tracking user activity online as the user moves between apps or websites. In particular, we present a new type of device fingerprinting attack, the factory calibration fingerprinting attack, that recovers embedded per-device factory calibration data from motion sensors in a smartphone. We investigate the calibration behaviour of each sensor and show that the calibration fingerprint is fast to generate, does not change over time or after a factory reset, and can be obtained without any special user permissions. We estimate the entropy of the calibration fingerprint and find the fingerprint is very likely to be globally unique for iOS devices (~67 bits of entropy for iPhone 6S) and recent Google Pixel devices (~57 bits of entropy for Pixel 4/4 XL). By comparison, the fingerprint generated by previous work has at most 13 bits of entropy. Following our disclosures, Apple deployed a fix in iOS 12.2 and Google in Android 11. Both code obfuscation and factory calibration help to hide software and hardware idiosyncrasies from third-parties, but this dissertation demonstrates that reliable software and hardware fingerprints can still be generated given sufficient knowledge and a suitable approach. Our work has significant practical implications and can be used to improve platform security and protect user privacy.