The article attempts to answer the following questions: What criminal law, if any, is applied in outer space when a crime is committed there? How will the issues of demarcation of criminal jurisdiction be resolved? Who and how will investigate such crimes? Which international or national institution will decide the issue of criminal prosecution and application of sanctions for crimes in space? Basing on the analysis of the sources of space and international law, it was concluded that today there is (...) no detailed procedure for investigating and bringing to criminal responsibility for committing a crime in space. There is also no international legal act that would establish a list of space criminal offenses. To solve existing problems, it is suggested to adopt the Convention on Criminal Liability for Space Crimes and to create a Space Criminal Statute (code). The article also claims that the creation of a World Space Union on regulating the commercial space activities will help in solving many issues in the field of research. (shrink)