Technology downscaling is expected to amplify a variety of reliability concerns in future digital systems. A good understanding of reliability threats is crucial for the creation of efficient mitigation techniques. This survey performs a systematic classification of the state of the art on the analysis and modeling of such threats, which are caused by physical mechanisms to digital systems. The purpose of this article is to provide a classification tool that can aid with the navigation across the entire landscape of reliability analysis and modeling. A classification framework is constructed in a top-down fashion from complementary categories, each one addressing an approach on reliability analysis and modeling. In comparison to other classifications, the proposed methodology approaches the target research domain in a complete way, without suppressing hybrid works that fall under multiple categories. To substantiate the usability of the classification framework, representative works from the state of the art are mapped to each appropriate category and are briefly analyzed. Thus, research trends and opportunities for novel approaches can be identified.