Well, you had successive waves Turco-Mongol, Iranian, and Uralic steppe nomads from the east, and nomadic groups like the Huns, of obscure easterly origins. The Berber tribesmen that invaded and settled Iberia were described being greatly diverse, ranging from dark-skinned "Ethiopians" to pasty white blondes. The Uralic peoples of Northern Europe looked (and still do) look different from most continental Europeans, and northern and eastern European Germanic and Slavic tribes had accured East Eurasian ancestry as a result of their interactions with groups like the Uralic/Finn-Ugric tribes, and Turkic and Mongolic groups, and long-admixed Scythian and other Iranian tribes, and Islamic settlement in portions of Southern Europe, such as Sicily, Malta, and even southern Italy and France all show a fairly diverse picture of early Middle Ages Europe. But nonetheless, using our modern western construct of race, all the above groups eventually came to largely be assimilated to what was likely a much larger indigenous European population and did not really change the genetic and phenotypic makeup of Medivial Europeans, and invading and migrating groups were likely dwarfed by the indigenous European populations they encountered, as we see in Al-Andalusia, Mongolian-ruled East Europe, the Bulgar settlement of the Balkans, and Tartar harrying of the Polish-Lithuanian state. The impact of some of these groups doesnt usually stem from their dominance in numbers, but moreso as small minorities with elite status whose dominance came in their sociocultural and ethnolonguistic identities and accompany military prowess. Some of these groups had very strong impact on the continent, accultrating entire indigenous European populations as we see in the creation of the Bulgarian ethnic group as a result of migrating Turkic Bulgars into the Balkans acculturating and fusing with a settled European population, the ascendancy of Arabic and Islamic culture in Al-Andalus and Sicily and its superior regard in the eyes of many Christian Europeans, and the adoption of Hunnic steppe customs by Germanic tribes like the Ostrogoths, Saxons, and others during the height of the Hunnic invasions and power in Europe, the acculturation of Central European populations to the identities and culture of Uralic steppe migrants leading to the formation of the Hungarian ethnic group, and the Turkificiation and Arabization of indigenous European populations, such as gradual Turkic acculturation of Eastern European Uralic Volga tribes, or the fact that the vast majority of indigenous Iberian Europeans in Al-Andalus either spoke a heavily Arabized Mozarabic tongue and were increasingly shifting over to speaking Arabic, forming the Andalusi Arabic dialect. in addition to this ~80% of indigenous Iberians in Al-Andalus (likely the majority of all indigenous Iberians) were Muslims, who along with the Berber settlers came to increasingly identify as Arabs and Arab Muslims, and not with their Celtiiberian, Germanic, and Romanance Iberian ancestries - and the for the Berbers, their Berber ancestry.

But if we speak of pre-historic Europeans, the picture is one of vast phenotypic diversity, with multiple phenotypically differentiated populations inhabiting the European continent, with Western European Hunter-gatherers, Eastern European Hunter-gatherers, A massive influx of Middle Eastern farmers from the Levant, North African immigrants in Spain, sub-Saharan populations who likely crossed over the Mediterranean into Europe, and a wave of East Eurasian migrants from eastern Siberia/China into Scandinavia and Eastern Europe. Then came the Yamnaya proto-Indo-European tribes from the shores of the Black Sea and Pontic steppe who added new genetic component to an already diverse Europe, and with their migrations into Europe proper, proceeded to assimilate the early European populations of diverse origins into the Indo-European fold, with earlier pre-I.E. languages largely going extinct minus Basque, Uralic tongues of Scandinavia and the Baltic. Heavy admixture between the wide array of groups over several thousands of years led to the development of a largely homogenized ancestral continent-wide European population, with a range of 30-90% Middle Eastern ancestry, and anywhere between 50-1% Yamnaya ancestry, and 60-1% East Eurasian ancestry. The present-day indigenous European phenotype and its diversity of skin hues, eye shapes, and hair color are all testament to this ages-old mingling between the various peoples of Old Europe.