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We first discuss Uraltsev's and other sum rules constraining the $B \toD^{**}(L=1)$ weak transitions in the infinite mass limit, and compare them withdynamical approaches in the same limit. After recalling these well establishedfacts, we discuss how to apply infinite mass limit to the physical situation.We provide predictions concerning semi-leptonic decays and non-leptonic ones,based on quark models. We then present in more detail the dynamical approaches:the relativistic quark model \`a la Bakamjian-Thomas and lattice QCD. Wesummarise lattice QCD results in the infinite mass limit and compare them tothe quark model predictions. We then present preliminary lattice QCD resultswith finite $b$ and $c$ quark masses. A systematic comparison between theoryand experiment is performed. We show that some large discrepancies existbetween different experiments. Altogether the predictions at infinite mass arein fair agreement with experiment for non-leptonic decays contrary to whathappens for semileptonic decays. We conclude by considering the prospects toclarify both the experimental situation, the theoretical one and the comparisonbetween both.

In Memoriam Nikolai Uraltsev : Uraltsev's and other Sum Rules, Theory and Phenomenology of $D^{**}$'s