A peculiar effect happens in air when laser pulses reach crazy-high intensities. The pulses start to get focused inward by the effect of the light on the air itself. The laser pulses are saved from catastrophic over-focusing by starting to make a plasma out of the air when their intensity gets too high, which acts to de-focus the beam. So we have a stable system with feedback - not intense enough? Then there’s not enough plasma to compensate for the self-focusing and the beam converges. Too intense? Then there’s an excess of plasma and the beam spreads out a bit. This self-focusing lets the beam overcome the diffraction limit. You end up with an inner core of sparsely ionized plasma surrounded by a sheath of high intensity light. 
These self-focused laser pulses, called laser filaments, have some really out there properties. Filaments tend to converge on a size of around 0.1 mm diameter and a power of 10 GW. If a filament gets more power than that, it will split into more filaments to keep the power down. If it has less power and there are other nearby filaments, it will merge with those filaments to bring its power back up.   Adjacent filaments tend to attract each other and propagate together as tight bundles.
Filaments cause ionization, so they lose energy to the air the farther they go. Their range depends on the energy in the pulse – the power per filament may be fixed, but longer duration pulses can have more energy. Roughly, a filament will lose about 2 μJ / m. But there’s an upper limit to the energy of a filament, too. If the duration is longer than about a picosecond, the electrons the laser pulse creates will have time to accelerate in the pulse’s electric field and crash into other atoms, freeing more electrons which will in turn make even more electrons - a runaway process called cascade ionization. If this happens, the plasma will absorb all of the pulse’s energy. If you send another pulse through before the old plasma has had time to recombine, that pulse could be blocked as well. It takes about 10 ns for the plasma to recombine enough to send another pulse after it.
So with 10 GW of power and 1 ps maximum duration, individual filaments won’t have more than 0.01 J or so, and thus they won’t get much farther than 5 km. High powered pulses that split into multiple filaments can go further by having the depleted filaments combine into full power filaments again. Keep in mind that these numbers are all extremely rough, but they give an idea of the order of magnitude of the timing and energies of these things.
Laser filaments are visible as bright streaks. This lets you see where you are shooting, but also lets your enemies see where you are shooting from. if you have visions of traditional Sci Fi media in your head, you might imagine these streaks starting at the end of your gun where the laser comes out, and ending at your target going all explody on you. But for several reasons this is probably not how it will go. First of all, you don't need to do it this way - just like with normal beams that start out wide and focus down to a tight intense spot, you can make your beams begin wide and only focus to an intensity that can initiate filamentation when the beam gets sufficiently focused. This lets you start the filament close to your target. And if you do this, then less energy is wasted making a long plasma in the air, leaving more to blast your target. You also don't have to worry about your pulse running out of energy before it even gets to the target. It makes it harder for your enemies to trace the filaments back to you. And perhaps most important is a technical issue – you probably can't design optics that can withstand the intensity of a filamenting beam, but you can make optics that can deal with the intensities of a widely expanded beam that can still initiate filamentation once it is focused down to a small spot.
If you have read the page on diffraction, you might think that this will limit the range at which you can get filamentation started based on the requirement for your laser to focus down to a minimum diffraction-limited spot size to start the filament. It turns out, this is not quite how it works. If you do the math, any beam that has enough power to start a filament (even if it does not have the intensity) will self focus enough when it gets into nearly-straight part of the beam (called the beam waist) to keep focusing so that the beam never expands again, but continues to contract down to a filament. If the beam has a wider minimum spot size, it also has a longer beam waist, giving more distance for the self focusing to take effect.
If you can get filaments, you can overcome the problems inherent in the limited depth of focus of laser beams, because once the filaments start they won’t spread out again.
The limitation on the maximum duration of a pulse before it stops filamenting and starts causing breakdown via cascade ionization, combined with the maximum intensity of a filament, might make it difficult to deliver enough energy to a target to have an effective weapon. One potential solution is to use a ring of filaments to guide a longer duration and higher energy pulse but with power below the filament threshold. Basically, if you make filaments in a cylinder and leave a core of normal air in the middle, the air will act like a fiber optic line and keep your laser beam from expanding due to diffraction or, potentially, thermal blooming  
Author: Luke Campbell
S. L. Chin, “Some Fundamental Concepts of Femtosecond Laser Filamentation”, Journal of the Korean Physical Society, Vol. 49, No. 1, July 2006, pp. 281-285.
Alexander L. Gaeta, “Collapsing Light Really Shines”, Science Vol. 301 pp. 54-55, 4 July 2003
Experiment demonstrates continuously operating optical fiber made of thin air
A. Goffin, A. Tartaro, and H. M. Milchberg, "Quasi-steady-state air waveguide", Optica Vol. 10, Issue 4, pp. 505-506 (2023).