The colonization of Europe by anatomically modern humans (AMH, technically Homo sapiens) is generally accepted to be clear with the rapid Aurignacian expansion, c. 41-40 millennia ago (kya). But the real implications of the MP-UP transition are often controversial.
In this sense, John F. Hoffecker has made a nice review of the matter, to which I've been directed twice in the last weeks by Dienekes and Tim respectively, and that I feel it's about time to comment on here as well.
John F. Hoffecker, The spread of modern humans in Europe. PNAS, 2009.
The author reviews in few pages the available data on the MP-UP transition in Europe and their possible relations with each of the human species extant at the time.
In the conclusion, he argues for two waves of AMH colonization of Europe: first, beginning c. 48 kya, the Bohunician (that for him includes Bachokirian), that would originate in the Emirian culture of Levant, extending into the East Balcans, parts of Central Europe and even Eastern Europe. Second would be the proto-Aurignacian, originating in the Ahmarian culture (derived from Emirian) and extending specially southern European areas, like Italy and the Pyrenees. The Aurignacian proper would be a European culture, possibly originated in the Balcans (though others have argued Central Europe).
Let's review the sequence and groups in more detail:
Group A: would include the Szletian (Central Europe) and Chatelperronian (Western Europe) cultures. At least the later is clearly associated with Neanderthal remains and, by extension, many believe that Szletian would be too.
Group B: would include the Bohunician (SE, Central and Eastern Europe) and its possible ancestor the Emirian of the Near East (specially the sites of Bocher Tachtit in Palestine, Ksar Akil in Lebanon and Üçagizli in southern Turkey). The Bohunician dates to c. 48 kya (Bacho Kiro, Bulgaria) and the latest dates are of c. 40 kya. There are no clear forsenic remains associated to it but some indications of it being of AMH creation are the presence of ornaments in some sites and the relation between Emirian and Ahmarian, this one clearly product of H. sapiens.
Group C: would include the proto-Aurignacian of Bulgaria (Temnata) Italy, Pyrenees and other southern European sites (and even Kostenki 14 in Eastern Europe) and the Ahmarian of the Near East. This one is clearly the product of AMH and Hoffecker argues that some of the oldest H. sapiens remains of Europe (Pestera cu Oase and others in Rumania) could belong to this techno-cultural group, even if they are devoid of any direct artifactual associations. Some Italian proto-Aurignacian also shows personal ornaments and bone industry, which again suggest AMH manufacture. The proto-Aurignacian dates to c. 45-40 kya.
The Uluzzian of Italy (since c. 48 kya) again is not directly associated to any particular human species. For this reason many think it could be a Neanderthal creation. But Uluzzian shows again personal ornaments and bone industry and could therefore be associated to H. sapiens on mere cultural grounds.
The Kostenki culture of Eastern Europe (since c. 44 kya) is clearly of AMH creation and, while original, shows occasional similitudes with Italian proto-Aurignacian (Kostenki 14) and the later Aurignacian. It is rich in bone industry and includes the first eyed needles known.
The Aurignacian. Hoffecker suggests a Balcanic origin for this culture though it's best documented first in Central Europe (c. 40-38 kya), overlying the transitional industries. It is possible that its expansion was favored by the Campanian Ignimbrite eruption, the most catastrophic volcanic event in the area in some 200 milennia, which is dated to c. 40 kya. Guess it could be included in group C.