Bianchi subgroups are cofinite non-cocompact lattices in PSL_2(C), defined by \Gamma_d = PSL_2(O_d), where O_d is the ring of integers of the imaginary quadratic field of discriminant -d. The Bianchi orbifold \Omega_d = \Gamma_d\H^3 is known to contain infinitely many immersed totally geodesic surfaces, which can be identified with integral binary hermitian forms over O_d. In this talk, I will show that some of these immersed totally geodesic surfaces are in fact orientable embedded closed totally geodesic surfaces using number theoretic ideas. I then present some numerical data concerning these surfaces. This talk is based on a joint work with Alan Reid and on an ongoing project with Sam Kim and James Rickards.