Space warfare
Currently, military operations in space primarily concern either the vast tactical advantages of satellite-based surveillance, communications, and positioning systems or mechanisms used to deprive an opponent of said tactical advantages.

Accordingly, most space-borne proposals which would traditionally be considered "weapons" (a communications or reconnaissance satellite may be useful in warfare but isn't generally classified as a weapon) are designed to jam, sabotage, and outright destroy enemy satellites, and conversely to protect friendly satellites against such attacks. To this end, the US (and presumably other countries) is researching groups of small, highly mobile satellites called "microsats" (about the size of a refrigerator) and "picosats" (approximately 1 cubic foot (≈27 litres) in volume) nimble enough to maneuver around and interact with other orbiting objects to repair, sabotage, hijack, or simply collide with them.

Kinetic bombardment: Another theorized use involves the extension of conventional weaponry into orbit for deployment against ground targets. Though international treaties ban the deployment of nuclear missiles outside the atmosphere, other categories of weapons are largely unregulated. Traditional ground-based weapons are generally not useful in orbital environments, and few if any would survive re-entry even if they were, but as early as the 1950s, the United States has toyed with kinetic bombardment, i.e. orbiting magazines of non-explosive projectiles to be dropped onto hardened targets from low Earth orbit.Kinetic weapons have always been widespread in conventional warfare—bullets, arrows, swords, clubs, etc.—but the energy a projectile would gain while falling from orbit would make such a weapon rival all but the most powerful explosives. A direct hit would presumably destroy all but the most hardened targets without the need for nuclear weapons.
Such a system would involve a 'spotter' satellite, which would identify targets from orbit with high-power sensors, and a nearby 'magazine' satellite to de-orbit a long, needle-like tungsten dart onto it with a small rocket motor or just dropping a very big rock from orbit (such as an asteroid, cf. Ivan's hammer). This would be more useful against a larger but less hardened target (such as a city). Though a common device in science fiction, there is no publicly available evidence that any such systems have actually been deployed by any nation.

Directed-energy weapons: Weapon systems that fall under this category include lasers, linear particle accelerators or particle-beam based weaponry, microwaves and plasma-based weaponry. Particle beams involve the acceleration of charged or neutral particles in a stream towards a target at extremely high velocities, the impact of which creates a reaction causing immense damage. Most of these weapons are theoretical or impractical to implement currently, aside from lasers which have been used to blind satellites and are starting to be used in terrestrial warfare. That said, directed-energy weapons are more practical and more effective in a vacuum (i.e. space) than in the Earth's atmosphere, as in the atmosphere the particles of air interfere with and disperse the directed energy. Nazi Germany had a project for such a weapon, considered a wunderwaffe, the sun gun, which would have been an orbital concave mirror able to concentrate the sun's energy on a ground target.
In the context of space-based deployment, directed-energy weapons can be distinguished as either “high-powered” or “dazzler.” High-powered satellite-operated lasers are intended to deal irreversible damage to the sensitive parts, mainly optics, on satellites and have the advantage of being difficult to attribute to an actor. Though, it is difficult to confirm the success of an attack. Dazzlers are not intended to deal irreversible damage but rather disable a target satellite. It maintains the same advantages and disadvantages as the high-powered variant. Though such systems not yet functional, the US Defense Intelligence Agency notes that several actors, including the United States, PRC, Russia, and France, are actively pursuing these capabilities.

Practical considerations: Space warfare is likely to be done at far larger distances and speeds than combat on Earth. The vast distances pose big challenges for targeting and tracking, as even light requires a few seconds to cover hundreds of thousands of kilometers. For example, if trying to fire on a target at the distance of the Moon from the Earth, one sees the position of the target slightly more than a second earlier. Thus even a laser would need ~1.28 seconds, meaning a laser-based weapon system would need to lead a target's apparent position by 1.28×2 = 2.56 seconds. A projectile from a railgun recently tested by the US Navy would take over 18 hours to cross that distance, if it travels in a straight line at a constant velocity of 5.8 km/s along its entire trajectory.
Three factors make engaging targets in space very difficult. First, the vast distances mean that an error of even a fraction of a degree in the firing solution can mean a miss by thousands of kilometers. Second, spaceflight involves tremendous speeds by terrestrial standards—a geostationary satellite moves at  3.07 km/s, and objects in low Earth orbit move at ~8 km/s. Third, though distances are huge, targets remain relatively small. The International Space Station, currently the largest artificial object in Earth orbit, measures slightly over 100m at its largest span. Other satellites can be vastly smaller, e.g., Quickbird measures only 3.04m. External ballistics for stationary terrestrial targets is enormously complicated—some of the earliest analog computers were used to calculate firing solutions for naval artillery, as the problems were already beyond manual solutions in any reasonable time—and targeting objects in space is far harder. And, though not a problem for orbital kinetic weapons, any directed energy weapon would need huge amounts of electricity. So far the most practical batteries are lithium, and the most practical means of generating electricity in space is photovoltaic modules, which are currently only up to 30% efficient, and fuel cells, which have limited fuel. Current technology might not be practical for powering effective lasers, particle beams, and railguns in space. In the context of the Strategic Defense Initiative, the Lawrence Livermore National Laboratory in the United States worked on a project for expandable space-based x-ray lasers powered by a nuclear explosion, Project Excalibur, a project canceled in 1992 for lack of results. SDI projects included Zenith Star, using the Alpha chemical laser.
General William L. Shelton has said that in order to protect against attacks, Space Situational Awareness is much more important than additional hardening or armoring of satellites. The Air Force Space Command has indicated that their defensive focus will be on "Disaggregated Space Architectures".

Space debris: Anti-satellite attacks, especially ones with kinetic kill vehicles, can form space debris which can stay in orbit for many years and could interfere with future space activity or in a worst case trigger Kessler syndrome. In January 2007 China did a satellite knock out whose detonation alone caused more than 40,000 new chunks of debris with a diameter > 1 cm and a sudden increase in the total amount of debris in orbit. The PRC is reported to be developing "soft-kill" techniques such as jamming and vision kills that do not generate much debris.

Possible warfare over space: Most of the world's communications systems rely heavily on the presence of satellites in orbit around Earth. Protecting these assets might seriously motivate nations dependent upon them to consider deploying more space-based weaponry, especially in conflicts involving advanced countries with access to space.
Since 2017, the United States Air Force has run an annual military exercise called "Space Flag" at Peterson Space Force Base, which involves a red team simulating attacks on U.S. satellites.
Robert Zubrin, aerospace engineer and advocate for human exploration of Mars, stated that anti-satellite weapons capabilities of nations increases, space infrastructures must be able to defend itself using other satellites that can destroy such weapons. Or else, he states, satellite-based navigation, communications and reconnaissance capabilities would be severely limited and easily influenced by adversaries.: 63–66

Direct Ascent: The modern incarnations of the ASM-135 ASAT program are the so-called direct-ascent anti-satellite weapons. These weapons are usually either ballistic or anti-ballistic interceptor missiles, which ascend directly from Earth to intercept their target and have  been adapted to the anti-satellite role. To date, four countries have demonstrated their ability to launch these weapons, the USA, the PRC, India, and Russia, but so far none have conducted such an attack on another country’s satellites.
Direct-ascent ASATs leverage existing technologies and launch platforms to neutralize both space-based and ground-based targets. This option tends to be highly destructive and indiscriminate as any attack will produce space debris, which can indiscriminately affect other satellites in similar orbits. While this option comes with the benefit of leveraging existing technologies and a certain element of surprise, as an attack cannot be detected until a missile has exited its silo, there are significant downsides. Firstly, there is the cost disparity of using an ICBM or ABM to kill a small and inexpensive satellite. Additionally, these missiles are not designed to send payloads out to geocentric orbit, as such they can only affect targets in low earth orbit and only in a target area centered around the static location of the missile itself.

Co-Orbital: Co-orbital systems come with a few potential kill mechanisms: in guided kinetic vehicles, like the Multiple Kill Vehicle, or in the form of a satellite that can release a kinetic interceptor or a cloud of debris.