Inverse methods form the basis of many investigations of the structure of the lithosphere-asthenosphere system as they provide the basis for physics-based subsurface imaging from surface and/or near-surface measurements. Steady increases in computational capabilities and methodological improvements have resulted in increasingly detailed three-dimensional models of the Earth based on inverse methods. While these models can show an impressive array of features, it may be difficult for non-specialists to assess which aspects can be considered reliable and which are tenuous, or are artefacts of the mathematical formulation or data collection. In this paper we address the fundamental issues of feature reliability due to limited resolution and model sensitivity to data noise for researchers who do not work with intimately with inverse methods. We include and introductory overview of the mathematical formulation of inversion methods and define commonly used terms and concepts. We then present two case studies based on data from USArray in the western United States. The first case study utilizes magnetotelluric array data to construct a three-dimensional model of electrical resistivity to a depth of approximately 300 km. We use this example to demonstrate fundamental issues regarding data fit, data coverage, and model parameterization. The second case study discusses how we can incorporate petrological and mineral physics information directly into the inversion approach to create models that are compatible with constraints on the temperature and composition of the lithosphere. We will discuss the implications for practical use of these models in interpretations and provide guidelines on how to evaluate such models.