Tevatron is soon expected to provide the first result for the frequency of the oscillations in the $B_s$--$\overline B_s$ system. To make this a good case for testing the hadronic sector of the Standard Model it is important to provide a sufficiently reliable theoretical prediction. I discuss the status and prospects to do that by computing the relevant matrix elements by means of the QCD simulations on the lattice, as well as by using the QCD sum rules. In the second part of this talk I present the first lattice QCD results for the relevant hadronic matrix elements which include the elegant solutions to circumvent the problem of spurious mixing in the renormalisation of the $\Delta B=2$ operators.

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