Were soldiers with these guns deployed alongside troops with swords and shields, or did handguns almost immediately replace things like pole arms as a primary weapon?

It was a slow process. At first, guns were adopted as a minor weapon alongside the others in use (an additional weapon, rather than a replacement for anything). Over time, guns became more common, and eventually became the main infantry weapon. Even then, they were still being used alongside pikes. It was the bayonet that led to guns replacing polearms, by allowing guns to be part-time polearms; this happened about 1700 (in Europe).

How slowly? Let's look at a timeline for European handguns:

• Mid 14th century (?) - first handguns in Europe.

• Late 15th century - guns are being used alongside crossbows as one missile weapon among others (some nice pictures showing this can be found in the Amtliche Berner Chronik (Official Chronicle of Bern)).

• Start of the 16th century - the pikeman is the king of the battlefield, but the matchlock arquebus, an improvement on earlier guns fired by a hand-held match, is making guns more important on the battlefield.

• The 16th century - in the first third of the 16th century, the shot (i.e., soldiers with handguns) often made up 30% of infantry formations, with most of the rest being pikemen. By the late 16th century, it was common for over half of the infantry to have guns; pikeman had become a minority.

• The 17th century - by the mid 17th century, 2/3 to 3/4 of the infantry were often musketeers. As the flintlock replaced the matchlock, and the bayonet was adopted, armies started getting rid of their pikemen completely. By the end of the 17th century, the pike was gone, and the gun had replaced the older infantry weapons.

So, in Europe, the replacement of other infantry weapons by the gun took about 350 years.

A Chinese timeline would be:

• 12th century - handguns probably in use

• 13th century - handguns certainly in use

• Late 14th century - early Ming armies have about 25% of their soldiers using firearms (this includes cannons; handgunners might have made up about 10% of the army).

• Mid 15th century - about 20% of Ming soldiers were handgunners.

• Early 17th century - about 40% of Ming soldiers were arquebusiers.

• Mid 18th century - over half of Qing soldiers were musketeers.

• Early 19th century - about 2/3 of Qing soldiers were musketeers.

In the mid 19th century, the Qing began to modernise their army, with modern rifles to become the standard infantry weapon. This took time to be completed (into the 20th century), but we can the mid 19th century as the time when the gun replaced other infantry weapons. Thus, the gun took 600-700 years to replace other infantry weapons in China.