There is now considerable evidence that in Europe, babesiosis is an emerging infectious disease, with some of the causative species spreading as a consequence of the increasing range of their tick vector hosts. In this review, we summarize both the historic records and recent findings on the occurrence and incidence of babesiosis in 20 European countries located in southeastern Europe (Bosnia and Herzegovina, Croatia, and Serbia), central Europe (Austria, the Czech Republic, Germany, Hungary, Luxembourg, Poland, Slovakia, Slovenia, and Switzerland), and northern and northeastern Europe (Lithuania, Latvia, Estonia, Iceland, Denmark, Finland, Sweden, and Norway), identified in humans and selected species of domesticated animals (cats, dogs, horses, and cattle). Recorded cases of human babesiosis are still rare, but their number is expected to rise in the coming years. This is because of the widespread and longer seasonal activity of Ixodes ricinus as a result of climate change and because of the more extensive use of better molecular diagnostic methods. Bovine babesiosis has a re-emerging potential because of the likely loss of herd immunity, while canine babesiosis is rapidly expanding in central and northeastern Europe, its occurrence correlating with the rapid, successful expansion of the ornate dog tick (Dermacentor reticulatus) populations in Europe. Taken together, our analysis of the available reports shows clear evidence of an increasing annual incidence of babesiosis across Europe in both humans and animals that is changing in line with similar increases in the incidence of other tick-borne diseases. This situation is of major concern, and we recommend more extensive and frequent, standardized monitoring using a “One Health” approach.