Given that sudden breakthroughs in conquering the cosmos are expected, some basic questions about the law governing relations in respect to outer space and in it can be expected to be triggered, starting already with the issue how one has to call that law and what is its real content. The first part of the paper deals with the naming of this branch of law and concludes that for the time being the term outer space law is the best and widely accepted. In the second part, the author states that many scientific papers and even official documents, do not define outer space law at all. There are even opinions that the outer space is a phenomenon which cannot be defined at all, suggesting that it is not possible to define a cosmic right either. The author considers that a distinction should be made between national space law of states and international space law (space law in the narrow sense a branch of international law containing legal rules governing relations in respect to the space and in the space, and in particular the regime of that space and celestial bodies it contains, exploration and exploitation of the space, the regime of navigation in the space, the legal position of the astronauts and space objects, international legal liability for damage caused by space activities, etc.). When so is clearly stated, one can also speak of space law in a broad sense, which, in addition to the norms of space law in the narrow sense, would include norms that are part of soft law, agreements and legal customs between states and non-state entities, and even at some point so-called. metalaw (law that may one day govern relations between humanity and creatures of other worlds).