Symmetries of the plane/space given by rational functions come with the basic mathematical structure of a group. This group, known as the plane/space Cremona group, is huge. One way to understand this group better is to classify all its finite subgroups. For the plane Cremona group, this was done Igor Dolgachev, Jeremy Blanc and Vasily Iskovskikh two decades ago, who classified finite subgroups of the plane Cremona group up to isomorphism. We intend to obtain some progress in this direction for the space Cremona group (real and complex), which is a much more difficult task.