  In this Colloquium, the wavefunction-based Multiconfigurational
Time-Dependent Hartree approaches to the dynamics of indistinguishable
particles (MCTDH-F for Fermions and MCTDH-B for Bosons) are reviewed. MCTDH-B
and MCTDH-F or, together, MCTDH-X are methods for describing correlated quantum
systems of identical particles by solving the time-dependent Schr\"odinger
equation from first principles. MCTDH-X is used to accurately model the
dynamics of real-world quantum many-body systems in atomic, molecular, and
optical physics. The key feature of these approaches is the time-dependence and
optimization of the single-particle states employed for the construction of a
many-body basis set, which yields nonlinear working equations. We briefly
describe the historical developments that have lead to the formulation of the
MCTDH-X methods and motivate the necessity for wavefunction-based approaches.
We sketch the derivation of the unified MCTDH-F and MCTDH-B equations of motion
for complete and also specific restricted configuration spaces. The strengths
and limitations of the MCTDH-X approach are assessed via benchmarks against an
exactly solvable model and via convergence checks. We highlight some
applications to instructive and experimentally-realized quantum many-body
systems: the dynamics of atoms in Bose-Einstein condensates in magneto-optical
and optical traps and of electrons in atoms and molecules. We discuss the
current development and frontiers in the field of MCTDH-X: theories and
numerical methods for indistinguishable particles, for mixtures of multiple
species of indistinguishable particles, the inclusion of nuclear motion for the
nonadiabatic dynamics of atomic and molecular systems, as well as the
multilayer and second-quantized-representation approaches, and the
orbital-adaptive time-dependent coupled-cluster theory are discussed.
