How can we reconstruct what long extinct animals, such as dinosaurs, looked like, how fast they moved, and what ecological role they played in their paleoenvironment? These features are not preserved in the fossil record, so paleontologists must instead turn to scientifically informed models and analogies to try to answer these questions. In her celebrated book Models and Analogies in Science, Mary Hesse illustrates the concept of material analogy using the examples of homologies and analogies in biology. These two types of analogy have given rise to two different research programs in the project of reconstructing extinct life: the Phylogenetic Approach and the Functional Morphology Approach. In this chapter I show how each of these approaches has its own strengths and weaknesses, and argue instead for an Integrated Approach that makes use of both of Hesse’s types of analogy. I conclude by highlighting the importance of paying attention to model uncertainty, adequacy-for-purpose, and the whole organism in a paleoreconstruction.