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The recent discovery of double charm baryon states by the LHCb Collaborarionand their high precision mass determination calls for a comprehensive analysisof the nonleptonic decays of double and single heavy baryons. Nonleptonicbaryon decays play an important role in particle phenomenology since they allowto study the interplay of long and short distance dynamics of the StandardModel (SM). Further, they allow one to search for New Physics effects beyondthe SM. We review recent progress in experimental and theoretical studies ofthe nonleptonic decays of heavy baryons with a focus on double charm baryonstates and their decays. In particular, we discuss new ideas proposed by thepresent authors to calculate the $W$-exchange matrix elements of thenonleptonic decays of double heavy baryons. An important ingredient in ourapproach is the compositeness condition of Salam and Weinberg, and an effectiveimplementation of infrared confinement both of which allow one to describe thenonperturbative structure of baryons composed of light and heavy quarks.Further we discuss an ab initio calculational method for the treatment of theso-called $W$-exchange diagrams generated by $W^{\pm}$ boson exchange betweenquarks. We found that the $W^{\pm}$-exchange contributions are not suppressedin comparison with the tree-level (factrorizing) diagrams and must be takeninto account in the evaluation of matrix elements. Moreover, there are decayprocesses such as the doubly Cabibbo-suppressed decay $\Xi_c^+ \to p \phi$recently observed by the LHCb Collaboration which is contributed to only by onesingle $W$-exchange diagram.

Novel ideas in nonleptonic decays of double heavy baryons