How do modern militaries deal with lefthandedness?

I imagine in the days before firearms, it was largely inconsequential. Advantageous, even, since it presented a somewhat-novel stance in melee engagements.

I know some manufacturers make ambidextrous platforms for commercial sale, but I just realized I have no idea how this works in military service around the world.

Do southpaws just train different techniques for cycling bolts, dealing with ejection, etc? I'm assuming eye-dominance typically follows handedness; does that also present significant challenges?