Did armies entirely abandon bows and crossbows all at once? Or did they phase out their use slowly while using some sort of combined-arms approach? What sorts of roles would each weapon serve during this phasing out period?
A reply to /u/rikeus
My colleague /u/MI13 wrote a fantastic post here discussing the demise of the longbow in the English military, and many of the points raised there apply to other western European nations, too.
I wrote a bit more here about the 1560-1600 period in England where by 1595 the bow was no longer considered an acceptable weapon for a first-line formation. Longbowmen were categorized as unarmed by then, in the sense that they received no pay nor logistical benefits when deployed.
And here I wrote about the Swiss and rise of Spanish pike & shot formations under de Cordoba in the late 1490s, which had a lot to do in heralding a new era of warfare.
The Spanish commander Gonzalo Fernandez de Cordoba eventually invented a new fighting system called the colunellia which became the basis of the tercio where close-order coordination between firearms and pikes could beat the pike-heavy Swiss formations.
The Tercio system became widely copied, although it took some time for other belligerents to catch up to Spanish organization, experience, and quality.