From about 1200 a German knight order occupied what are now the Baltic states (Estonia, Latvia, Lithuania). They kept the overall control of these countries for several centuries and much of the population converted to Christianity.
At the same time, the Hanseatic League rose to power and became the dominant economic force in the Baltic Sea for several centuries. Its origins also lie in Germany, and its members played an important role in shaping the main cities in the Baltics (Riga, Tallinn, etc).
When I read up on either the crusades or the Hanseatic League I find a lot of information. What seems to be missing are connections: are there any links between both, and what are they?
There is not really a direct connection. While the North German trading towns and trading towns around the Baltic sea had been emerging by the point of the northern crusades, the crusades for Livonia and Estonia pretty much predate the formation of the Hanseatic League as it is mostly known (although again - trading towns, guilds and trading outposts did exist prior).
What connection there was, is that the northern crusades were certainly motivated among other things by money, and the the trade potential of the Baltic north-east - south-west trade routes was apparent in large part due to previous trade by future Hanseatic League towns. We also see, that for example in Reval/Tallinn/Lindanyse - after the conquest by Danes in 1219, the area was inhabited by merchants from Visby - an important trading town and an important Hanseatic town.
So rather than a direct connection, prior trading interests may have been a partial motivation for the crusades, and after the crusades, the emergence of newly christianised land provided the opportunity for merchants and the Hanseatic League to expand into Eastern Baltic.