1. The Treaty on Principles Governing the Activities of States in the Exploration and Use of Outer Space, including the Moon and Other Celestial Bodies (the "Outer Space Treaty")
The Outer Space Treaty is the most important of the five treaties, as it creates the framework for laws beyond our planet. Since going into effect in October 1967, 103 countries have signed the treaty, including the United States, Russia and the United Kingdom.
Among other things, parties to the treaty agree to keep space a peaceful, non-militaristic zone. They also agree not to send nuclear weapons into orbit around the Earth or on celestial bodies. And the treaty expressly prohibits the use of the moon and other celestial bodies for the "establishment of military bases, installations and fortifications, the testing of any type of weapons and the conduct of military maneuvers." Or, put more succinctly: There will be no Star Wars; the Mandalorians would most certainly be out; and member states have agreed not to use the likes of a thermal detonator.
2. The Agreement on the Rescue of Astronauts, the Return of Astronauts and the Return of Objects Launched into Outer Space (the "Rescue Agreement")
The Rescue Agreement went into effect in December 1968, and it elaborates on certain portions of the Outer Space Treaty. Specifically, it requires that all contracting parties, "prompted by the sentiments of humanity," take all reasonable steps to assist and/or rescue astronauts in distress and subsequently aid them in returning to their launch location. Which means that if the place where Dr. Ryan Stone landed had ratified the Outer Space Treaty, she could expect some help in getting back home.
The Agreement also stipulates that parties will assist in recovering space objects that return to Earth outside of the territory of a launching party.
3. The Convention on International Liability for Damage Caused by Space Objects (the "Liability Convention")
Like the Rescue Agreement, the Liability Convention was adopted to elaborate on the Outer Space Treaty -- specifically provisions on liability. Adopted in 1972, it established that a launching party is "absolutely liable to pay compensation for damage caused by its space objects on the surface of the Earth or to aircraft." And per the convention, "'damage' means loss of life, personal injury or other impairment of health; or loss of or damage to property of states or of persons, natural or juridical, or property of international intergovernmental organizations."
Essentially, the Liability Convention says that you can't just launch things into space and hope for the best. If two satellites collide or a damaged space station re-enters the atmosphere and crashes, someone is on the hook.
The convention also establishes that when two or more parties launch a space object together, they can be held independently liable for the full amount of the damages, regardless of a party's share.
4. The Convention on Registration of Objects Launched into Outer Space (the "Registration Convention")
Surprise, surprise: The Registration Convention deals with the registration of space objects. More specifically, parties to the convention are required to provide to the United Nations, as soon as possible: the name of launching state or states; an appropriate designator of the space object or its registration number; date and territory or location of launch; basic orbital parameters; and the general function of the space object.
5. The Agreement Governing the Activities of States on the Moon and Other Celestial Bodies (the "Moon Treaty")
And finally, there's the Moon Treaty, which explains how the provisions of the Outer Space Treaty would apply to the moon and other celestial bodies in the solar system. The ones other than Earth, at least.
In an effort to prevent the moon from becoming an area of conflict, the treaty requires that all exploration be exclusively for peaceful purposes. Parties agree not to establish military bases or test weapons on the moon. They agree not to place nuclear weapons or other weapons of mass destruction in orbit around the moon. And they pledge to take measures to protect the moon's existing environment.