The results made by the members of the Finnish Inverse Problems Society are significant to the field and have a number of potential applications. Especially, significant contributions has been made to the following subfields of inverse problems:

- Electrical impedance tomography, or imaging the interior of living tissue or process pipelines using electric measurements on the boundary of the target,
- Cloaking and electromagnetic wormholes,
- General purpose incoherent scatter radar measurements,
- Detection of space debris,
- Three-dimensional medical X-ray tomography, where the inner structure of a patient is imaged from a set of X-ray images,
- Recovering the shapes and spin states of asteroids from light curve data,
- Adaptive Markov Chain Monte Carlo methods,
- Statistical inverse problems.

For further information, see home pages of the Finnish Centre of Excellence in Inverse Problems Research.

The Inverse Problems International Association (IPIA) awards the Calderón Prize to a researcher under the age of 40 who has made distinguished contributions to the field of inverse problems broadly defined.

The first Calderón Prize was awarded to Matti Lassas, Professor of Applied Mathematics at University of Helsinki and the Great Diving Beetle of the Finnish Inverse Problems Society.

In 2013, the Calderón Prize was awarded to Mikko Salo, a Professor of Mathematics at University of Jyväskylä and a member of the Finnish Inverse Problems Society.