Observing vertically resolved atmospheric states using remote sounding instruments – often called profile retrieval in short – requires estimating state vectors from under-constrained inverse problems. This is not straightforward, and therefore usually requires lots of implementational fine-tuning. This lecture discusses the information content studies and rigorous uncertainty analyses that allow understanding, evaluating, and refining the profile retrieval process. Examples are provided for ozone profile retrievals from nadir and limb viewing satellite instruments.