Many of the state-of-art approaches for detecting plagiarized or malicious Android applications and pinpointing bugs in automated Android application testing rely on semantic models of applications as abstractions of what the sample in question does or how it visually looks like. While similar or even identical models, e.g., control flow graphs and state machines, are often used across the literature, usage of certain abstractions in existing tools is mostly based on intuitions of the researchers designing the approaches and there is no established view on what could work for certain tasks or why does it work. In our project we plan to systematically investigate semantic application models used for malware and repackaging detection, and automated testing. We will propose a taxonomy for these models that will map and unify different abstractions and the behavioral aspects the abstractions are applied for. We will then design a formal framework that will allow to produce new semantic models incorporating the aspects required (i.e., representative of the relevant behaviors). The new models designed with the DroidMod framework will be validated in large-scale experiments in mobile and repackaging detection and automating testing on real apps. Thus we will improve the state-of-art in Android security and security and privacy of the Android users.