The proportion of Europeans descending from Neolithic farmers ~10 thousand years ago (KYA) or Palaeolithic hunter-gatherers has been much debated. The male-specific region of the Y chromosome (MSY) has been widely applied to this question, but unbiased estimates of diversity and time depth have been lacking. Here we show that European patrilineages underwent a recent continent-wide expansion. Resequencing of 3.7 Mb of MSY DNA in 334 males, comprising 17 European and Middle Eastern populations, defines a phylogeny containing 5,996 single-nucleotide polymorphisms. Dating indicates that three major lineages (I1, R1a and R1b), accounting for 64% of our sample, have very recent coalescent times, ranging between 3.5 and 7.3 KYA. A continuous swathe of 13/17 populations share similar histories featuring a demographic expansion starting ~2.1-4.2 KYA. Our results are compatible with ancient MSY DNA data, and contrast with data on mitochondrial DNA, indicating a widespread male-specific phenomenon that focuses interest on the social structure of Bronze Age Europe.