  The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method
and the density matrix renormalization group (DMRG) are powerful workhorses
applied mostly in different scientific fields. Although both methods are based
on tensor network states, very different mathematical languages are used for
describing them. This severely limits knowledge transfer and sometimes leads to
re-inventions of ideas well known in the other field. Here, we review ML-MCTDH
and DMRG theory using both MCTDH expressions and tensor network diagrams. We
derive the ML-MCTDH equations of motions using diagrams and compare them with
time-dependent and time-independent DMRG algorithms. We further review two
selected recent advancements. The first advancement is related to optimizing
unoccupied single-particle functions in MCTDH, which corresponds to subspace
enrichment in the DMRG. The second advancement is related to finding optimal
tree structures and on highlighting similarities and differences of tensor
networks used in MCTDH and DMRG theories. We hope that this contribution will
foster more fruitful cross-fertilization of ideas between ML-MCTDH and DMRG.
