  Higher-twist transverse momentum dependent parton distribution functions
(TMDs) are a valuable probe of the quark-gluon dynamics in the nucleon, and
play a vital role for the explanation of sizable azimuthal asymmetries in
hadron production from unpolarized and polarized deep-inelastic lepton-nucleon
scattering observed in experiments at CERN, DESY and Jefferson Lab. The
associated observables are challenging to interpret, and still await a complete
theoretical explanation, which makes guidance from models valuable. In this
work we establish the formalism to describe unpolarized higher-twist TMDs in
the light-front framework based on a Fock-space expansion of the nucleon state
in terms of free on-shell parton states. We derive general expressions and
present numerical results in a practical realization of this picture provided
by the light-front constituent quark model. We review several other popular
quark model approaches including free quark ensemble, bag, spectator and chiral
quark-soliton model. We discuss how higher-twist TMDs are described in these
models, and obtain results for several TMDs not discussed previously in
literature. This study contributes to the understanding of non-perturbative
properties of subleading twist TMDs. The results from the light-front
constituent quark model are also compared to available phenomenological
information, showing a satisfactory agreement.
