Summary: The search for plane geometric figures with integer or rational side lengths and/or areas has deep historical roots. For instance, the search for rectangular triangles with integer cathetuses and hypotenuse leads to the Pythagorean number triples. Another example is the so-called congruence number problem from the 7th century, i.e. the problem of the existence of rectangular triangles with rational side lengths and a given integer area, a problem which is still not completely solved to this day. The article treats the existence of quadrilaterals with rational sides and diagonals.The authors first of all remind the readers of Kummer’s parametrisation of such quadrilaterals using rational points on special elliptic curves, and then discuss certain degenerate cases which have been left out of consideration in Kummer’s work.