A graph is called intrinsically knotted (linked) if every embedding of
it in S^3 contains a nontrivial knot (link). In the early 1980's,
Sachs, and independently, Conway and Gordon, showed that K_6, the
complete graph on six vertices, is intrinsically linked. Conway and
Gordon also showed that K_7 is intrinsically knotted. In 1995
Robertson, Seymour, and Thomas classified all intrinsically linked
graphs by proving a conjecture of Sachs: a graph is intrinsically
linked if and only if it contains as a minor K_6 or a graph obtained
from K_6 by triangle-Y or Y-triangle moves. We will start with the
Conway and Gordon theorems and then go through a (partial) survey of
old and recent results and some open questions in the field.