The need to blend observational data and mathematical models arises in many
applications and leads naturally to inverse problems. Parameters appearing in
the model, such as constitutive tensors, initial conditions, boundary
conditions, and forcing can be estimated on the basis of observed data. The
resulting inverse problems are often ill-posed and some form of regularization
is required. These notes discuss parameter estimation in situations where the
unknown parameters vary across multiple scales. We illustrate the main ideas
using a simple model for groundwater flow.