After a gentle introduction to Borel classification theory, we shall discuss the complexity of the bi-embeddability relation in the case of various countable structures. In particular, we shall show that the bi-embeddability relation on ordered divisible abelian groups is as complicated as possible among analytic equivalence relations. As we will see, our results are connected with the model theory of o-minimal theories. In the end, we shall discuss some open questions that we hope to settle in the near future. This work is joint with D. Marker and L. Motto Ros and still in progress.