This journey through the fascinating world of molecular topology focuses on catenanes, rotaxanes and knots, their synthesis, properties, and applications and the theory of interlocking and interpenetrating molecules. Nearly one hundred years of progress have passed since Willstatter's speculative vision of a molecule consisting of two interlinked rings. But even today the synthesis of such structures are a challenge to the creativity of synthetic chemists. These molecules are not only of academic interest, since they occur naturally. In such molecules as DNA, knots and related topological features play a key role in biochemical processes. In addition, extensive research on the properties of polyrotaxanes and polycatenanes show potential applications as molecular magnets, wires or switches.