This article aims to reconstruct the history of ancient R1b migrations from 16,000 to 1,500 years before the present (rbp). Four thousand four hundred and eight (4408) haplotypes of the R1b haplogroup (with subclades) were considered in terms of the basal (ancestral) haplotypes of R1b populations and the calculated time to their common ancestors. The regions considered extend from southern Siberia/Central Asia in the east (where the R1b haplogroup arose around 16,000 bp) through northern Kazakhstan, the southern Urals to the Russian Plain and further west to Europe (the northern route entering Europe around 4,500 bp); from the Russian Plain south to the Caucasus (6,000 yr ago), Asia Minor (6,000 yr ago) and the Middle East (6,000-5,500 yr ago) to the Balkans in Europe (southern route, entering Europe about 4,500 yr ago); along North Africa and the Mediterranean (5,500-5,000 yr ago) through Egypt to the Atlantic, north to the Iberian Peninsula (North African route with reaching the Pyrenees 4,800 yr ago). The Arbinians (carriers of haplogroup R1b) along their migration route to the Middle East and southern Mesopotamia apparently established the Sumerian culture (and state), moving west to Europe (5000-4500 years ago), carrying mainly the R-M269 subclade and its further L23 subclade. The latter subclade was almost absent from the North African route and/or did not survive the migration to the Iberian Peninsula or its presence was confirmed later. Upon arrival on the Iberian Peninsula (4800 years ago), the M269 subclade separated from M51 and soon after from the lower L11 subclades. These populations became known as Bell's cup populations and moved north, along with the newly formed subclades P312 and L21 (which separated within a few centuries after P312). These subclades and their lower clades have effectively populated Europe without much interruption (smooth haplotype trees show almost uninterrupted proliferation of R1b haplotypes in Europe). They can be seen from the Atlantic eastward, through the Balkans, the Carpathians, present-day Poland, the western border of the Russian Plain and all the way to the Baltic Sea. The islands have had a different history of R1b migration. The carriers of L11, P312 and L21 came to the Islands by land and sea simultaneously with the Arbins, who settled Europe between 4000 and 2500 BC, creating the respective "local" subclades of P314, M222, L226, which largely settled the Islands. As a result, much of the Islands are inhabited almost exclusively by Arbins, whose prevalence reaches 85%-95% in the current population. Overall, the frequency of Arbins in Western and Central Europe reaches, albeit unevenly, about 60% of the population. This study essentially presents an example of the application of DNA genealogy in the study of human history.