There‘s also a type of caseless ammunition that would be electrically fired, so no firing pins nessecary, just something to make a spark.
From what I understand, the amunition is rectangular because you can make a more compact round with the same ammount of propellant. That saves space and weight, as well as allows for smaller magazines. (Take a rectangle and a cylinder of the same width, length, height etc... The clinder will be able to hold less propellant than the rectangle. So, you can shrink the rectangle and still have the same ammount of propellant as the cylinder)
Advantages? No casings to be ejected, which will in turn cause less jams. Higher rate of fire is also possible. No ejection port covers for dust to get into if you don‘t close it. You won‘t leave piles of brass for range control to yell, or for the enemy to find to know you where (are) there. Also with the smaller size and saved weight, it‘s easier to transport more ammo both for the individual troops, and for the logisitcal side.
Downsides? I‘m not sure how far the technology has come along, but it would have to burn the propellant completley, and the bonding would have to be tough (Say the round breaks in half inside of the chamber.) But these issues would have definatley been addressedby the designer...
You also won‘t be able to laugh at the person beside you when they get some of your brass down their shirt on the range anymore..
[Edited Note; I did some research, and due the nature of caseless, it burns much hotter than regular cased ammunition, ensuring that all the propellant is burnt off.]