I wear 46 in most Euro shoes.  The 44-45 fit me better barefoot. I don't wear socks with these. I did, however feel like each size (I tried 44-46) was too narrow for my wide feet. I didn't feel like that with the older KSO model I had (size 45).  But his does feel close to barefoot, and the material is lighter and breathes better. The adjustable laces help keep these on like skin, which is better than the older version, which could slip around under you.