I’ll try to answer your question, sorry if it doesn’t satisfy you. Ottoman raiders and Barbary corsairs frequently organize raids to capture and enslave people, this practice was at its peak in the 16th to 17th century but starting to wind down and almost disappeared by the 18th century. I’ll try to divide it by region, the Mediterranean by the Barbary corsairs and Eastern Europe by Ottoman raiders.

The Mediterranean – Barbary corsairs

In the 16th to the 17th century, slave-taking in the Mediterranean is something of a “custom”. Both Christian and Muslim pirates raided and took each other as slaves, where the taking of slave prisoners on the battlefield was seen as an achievement. Clashes and raids on land and sea between the Ottomans, the Habsburgs, and their respective allies brought thousands of slave captives to slave markets of the Mediterranean. However among all, the Barbary corsair stood out as the most effective slave-raiding force and one that continued the practice well into the 18th century. Every year, the Barbary fleet along with its captains set sail to fight and raid European shipping and coastal regions of Italy, Spain, and other Mediterranean regions. They occasionally sails into the Atlantic, and of course captured British, Dutch, or Danish shipping in the region but their main targets were the ones closer to their home shores and especially ones they had to fight frequently with: Spanish, Italian, Portuguese, and French sailors were frequently subjected to raids. One example of 16th century annual raid is one raid conducted by Hasan Pasha. Envious of a successful raid conducted by his colleague Murad Reis that brought 500 Spanish slaves seized from the coast of Alicante, Hasan raided the coasts of Sardinia, capturing 700 captives, then continuing to Monticello capturing 400, then Sori capturing 130, then finally on the coasts of Pineda capturing 50 before finally returned home. With the Ottoman-Habsburg conflict winding down, the Barbary raids yielded less captives compared to the previous century, though still numerous with numbers in the hundreds this time with little Ottoman direction. Although as you know the Barbary corsairs started to venture to the Atlantic, the Atlantic is only occasionally being targeted to raids because they yielded comparatively small number of captives compared to the Mediterranean or islands near their base. For example in 1613 the corsairs took 700 captives from Canary island, while a raid on Madeira in 1619 yielded 1,500 captives compared to the long raids on Iceland which only yielded 400 captives. On the Mediterranean, by the 17th century much of the coastline settlements had been abandoned or heavily fortified, making the corsairs targeted shipping more, which yielded more captives and loot. It has been calculated that in the first half of the 17th century the corsairs may have captured around 200 ships each year compared to 50 in the late 16th century. The numbers are still subject to contentious debate, but one estimate suggests that around 180,000 European captives were taken by the Barbary corsairs between 1574 and 1644

By the 18th century, corsairing activities had generally declined, mostly because the growing economic integration of North Africa into Ottoman and international commercial links which made the corsairs profit from shipping and trade, and so most European nations have generally made peace treaties with the Barbary states. However, the practice didn’t die out, and the corsairs have a principle of never be at peace with all the European states at the same time, including even those that had signed peace treaties with them lest the corsairing activities will cease. One prime example of this was the Dutch, who had signed a treaty in 1679. With the weakening of Dutch shipping, the corsairs started to target Dutch ships again, and between 1714 and 1720 the Barbary corsairs captured some 40 Dutch ships and 900 Dutch sailors. The Dutch then offered peace with increasing the tribute, which was signed in 1726. This kind of thing will happen on and off throughout the centuries, The Dutch were at war with the Barbary States from 1755 to 1757 and 1792 to 1794, and 1789 to 1791. However, in the end peace would always be concluded and shipping resumed as usual

Eastern Europe and the Black Sea – Ottoman and Tatar raiders

Tatar horsemen and raiders of the Crimean Khanate were the principal supplier and commercial agents of the Black Sea slave trade until the late 18th century. They launched frequent raids on Russian and Polish-Lithuanian settlements from the 16th century until their last raid in 1769 capturing perhaps 2 million people between 1500 and 1700. Tatars themselves suffered raids, and enslavement by Cossacks. There are two ways of obtaining slaves, either by capturing prisoners of war during warfare, or by raiding on settlements. Generally, Ottoman and Tatar soldiers were not supposed to kill captives with strong prospects of turning captives to the state for reward, selling them into slavery, or ransoming them. In many cases, Ottoman and Tatar soldiers kept and enslaved captives, either to be sold or used by themselves. For example, during the second Morean War, the state allowed soldiers to enslave and sell captured enemy soldiers. Another was during the Russo-Turkish war of 1768, where Russian captives were frequently sold as slaves. The second way is by raids. This was generally done by Crimean Tatars, though Ottoman raiders would also participate. Most successful raids were led by the Khan, kalga, or nureddin. Minor raids which happened most often were usually done twice a year, during harvests and winter. The raids against Russia and Poland were the most successful because the borders of these countries were open to the south and Russia especially was not in a position to militarily defend the population of a vast area, though Russia eventually learned their lessons and constructed strong fortifications in the area which helped quell Tatar raids. Example of such raid was in 1500, where 1,000 Tatar horsemen raided a Lithuanian village yielding 5,000 captives and on a Russian settlement in 1735 which yielded some 700-800 captives. These slaves were then sold by Crimean middlemen to the Ottoman Empire, The Caucasus, and Central Asia. Eventually however, these practices declined by the 18th century. By the 1780s, laws regarding prisoners of war had been accepted and guaranteed, making POWs only eligible for ransom and not slavery. Additionally, with the demise of the Crimean Khanate, such raids on Russian and Polish-Lithuanian settlements died out

Additionally, during the 16th and 17th century, raids for slaves also occurred between the Ottoman-Hungarian border. During wars, like in the war of 1522 or 1683 both sides captured large number of soldiers to be sold in slave markets of Sarajevo and Istanbul for the Ottomans, or sold to Austrian and Italian merchants for the Hungarians. During peacetime, sporadic skirmishes and raids conducted by both sides also yielded captives to be sold into slavery. More of course can be said on Hungarian raiders, but given the nature of your question, I’ll focus on Ottoman raiders. Ottoman raiders were usually martoloses, a kind of auxiliary militia or pribeks, Hungarian deserters that joined the Ottomans. In the course of attack, Ottoman raiders set out openly with flags unfurled to enemy territory to plunder the land. Captives were then taken to prisons, where their fate is determined based on birth and rank. If they’re of high status, they’ll usually be hold for ransom, but if not, they’ll be sold into slavery. Once they had been taken by their new owner, their only hope of freedom was by divine intervention, but there are some who escaped. Crimean Tatar troops that joined the Ottoman army also raided Hungarian settlements, but these was much rare, because the Ottomans frequently curbed Tatar abilities to devastate the region and the long distance involved to transport captives. One example of this Tatar raid (and the last) was from 1717 in Ugocsa, which yielded 861 captives.

Sources:

On Barbary Corsairs:

Lords of The Sea: A History of the Barbary Corsairs by Alan Jamieson

Christian Slaves, Muslim Masters: White Slavery in the Mediterranean, the Barbary Coast, and Italy, 1500-1800 by Robert Davis

Barbary Corsairs, The End of a Legend 1800-1820 by Daniel Panzac

On Eastern Europe:

Ransom Slavery along the Ottoman Borders edited by Suraiya Faroqhi and Halil Inalcik

From Slaves to Prisoners of War: The Ottoman Empire, Russia, and International Law by Will Smiley

Russia's Steppe Frontier by Michael Khodarkovsky