The era of NDE 4.0, characterized by the integration of cyber-physical capabilities into non-destructive evaluation (NDE), has put digital technologies such as modeling and simulation at the forefront of the field. This paradigm shift, while promising improved efficiency and reliability, highlights the critical challenge of establishing credibility in NDE models amidst an increasing reliance on computational tools. The field of uncertainty quantification (UQ) addresses this challenge by providing methodologies to understand the effects of the unknown in the modeling process, thereby instilling confidence in computational models within the context of NDE 4.0. This chapter gives a broad introduction to modern methods in UQ. Starting from a brief review of fundamental prerequisites, a general overview of primary UQ concepts is provided before discussing a survey of recent UQ approaches within the NDE field. Model-assisted probability of detection (MAPOD), a framework that combines simulated and empirical inspection data to generate POD curves, is adopted as a contextual example to relate UQ concepts to a practical NDE application. Over the course of the chapter, explicit connections between NDE problems and modern UQ solutions are established where these ties are often underreported, and several relatively unexplored areas of overlap are identified for future study.