My mother and I have always thought that my father's side of the family might carry a hint of Asian ancestry. I have done genetic testing with 2 different companies, and I was disappointed when both companies reported my ancestry as 100% European. Of course, these results were provided based on comparison of my genetic material to databases that continues to grow and to be refined. I was pleasantly surprised when one of the companies recently updated my results to tell me that I am 95.76% Western European (Orcadian) and 4.24% South Asian (Pathan /Pashtun, Southeast Indian, North Indian).
I still don't think this tells the whole story of my ancestry. My father's parents were both Ukrainian, so I would expect to see some Eastern European ancestry in the mix. I have reason to think that my great, great, great grandmother (maternal) was of Dutch ancestry, but I still don't know a lot about her. I'll keep searching!