Given a finite set of primes $S$ and a m-tuple $(a_{1},...,a_{m})$ of positive, distinct integers we call the m-tuple $S$-Diophantine, if for each 1 ≤ i < j ≤ m the quantity $a_{i}a_{j}+1$ has prime divisors coming only from the set $S$. In this talk we discuss the existence of m-tuples if the set of primes $S$ is small. We will discuss recent results concerning the case that $|S| = 2$ and $|S| = 3$.