Warfare in the 18th Century mentions that one of the reasons the British armies were able to do so well in India was that they didn't have a train of camp followers and so could march faster. As others point out there are people you could call "camp followers" even today but it looks like they stopped being integral to a marching army sometime between the early 17th and mid 18th centuries in Europe.
Western Armies increasingly tried to "in-source" their logistical operations over the course of the 18th and 19th centuries, especially as armies grew larger and simply "foraging" (aka stealing from local civilians) was grossly insufficient to supply an army on the move. Different military forces took different approaches to improving logistics, depending on their strategic situation.
Speaking in very general terms, the British, French, and Prussian militaries of the Napoleaonic era exmplify the three main appraoches taken toward managing military logistics:
The British approach was generally for each commanding officer in a given area to contract with local merchants and sutlers. This worked better for the navy than it did for the army, since armies were constantly on the move. British camp-followers of the early 19th century tended, on the whole, not to be the families of the troops, but indpentendt entruemeurs and subcontractors whom followed the armies of their own free will.
The Prussians had a centralized logistics officer in each canton who was responsible not only for feeding his regular troops but also for keeping a sufficient cache of supplies on hand to feed Prussian soldiers as they marched through. This system worked better than you might expect, especially since the military supply depots often helped stabilize the local price of grain. This system was build around the needs of an army that while large relative to the size of it's population, tended to fight short, decisive conflict relatively close to their home territory, and armies in the field usually had to resort to foraging if offensive operations lasted more than once season.
The French approach was to grant a monopoly on the selling of provision to official Vivandières" or "Cantinières", who were usually the wives of the soldiers. Under the Ancien Regime, officially, there were only supposed to be a maximum of eight Vivandieres and eight blanchisseuses ('laundresses') in each regiment. T In practice implementation varied considerably. Efforts to reform this system during the revolutionary period were ultimately unsuccessful, although by the era of the Crimean War, there's surprisingly egalitarian permutation where cantinieres (who were always female) were considered part of the army and were paid a wage on a scale similar to other enlisted personnel.
Here are a selection of past threads that explain this way better than I ever could: