Until today, I had never heard of Yandex. I do have to say that their search quality appears to be very high, and I may use them as a Google alternate in the future. Is there any specific reason why they don't have much traction in the US?
Yandex was created a bit earlier than Google actually.
Yandex specializes mostly on Russian-speaking countries and neighbours like Ukraine, Belarus, Kazakhstan. Recently Turkey.
AFAIK, they never tried to market the service in the US.