The inverse problem in mathematical biology

•Estimation of computational models of biological systems poses formidable challenges.•Mechanistic inference usually requires practical parameter identifiability.•Prediction of system evolution may not require parameter identifiability.•A satisfactory solution to the inverse problem awaits further theoretical progress.

Biological systems present particular challengers to model for the purposes of formulating predictions of generating biological insight. These systems are typically multi-scale, complex, and empirical observations are often sparse and subject to variability and uncertainty. This manuscript will review some of these specific challenges and introduce current methods used by modelers to construct meaningful solutions, in the context of preserving biological relevance. Opportunities to expand these methods are also discussed.