In the BMO theory of the universal Teichmüller space, some characterizations of the BMOA-Teichmüller space are well known. The authors give two more equivalent characterizations by using some kernel functions and corresponding operators induced by quasisymmetric homeomorphisms. Various equivalent characterizations of the VMOA-Teichmüller space are also given in this paper. The authors also prove that BMO-Teichmüller spaces have natural complex structures in different models, and this is applied to prove that if a homeomorphism \(h\) of \(S^1\) is absolutely continuous with \(\log h'\) belonging to \(\mathrm{VMO}(S^1)\), then \(\log f'\) belongs to \(\mathrm{VMOA}(\triangle)\), where \(f\) is a bounded conformal mapping on \(\triangle\) and \(h\) is the corresponding quasisymmetric conformal welding.