It is proved that the moduli space F_g of primitively polarized K3 surfaces S of degree 2g-2 is of general type for g >= 63 using its description as arithmetic quotient of a 19-dimensional bounded symmetric domain. Oppositely F_g is unirational for g =< 13 and g=17, 18, 20. Exceptional vector bundles and semi-exceptional ones give an explicit description of S in a certain homogeneous space or moduli space for such value of g. In this talk I will discuss this mainly in the case g=17.