  An approach for relating the nucleon excited states extracted from lattice
QCD and the nucleon resonances of experimental data has been developed using
the Hamiltonian effective field theory (HEFT) method. By formulating HEFT in
the finite volume of the lattice, the eigenstates of the Hamiltonian model can
be related to the energy eigenstates observed in Lattice simulations. By taking
the infinite-volume limit of HEFT, information from the lattice is linked to
experiment. The approach opens a new window for the study of
experimentally-observed resonances from the first principles of lattice QCD
calculations. With the Hamiltonian approach, one not only describes the spectra
of lattice-QCD eigenstates through the eigenvalues of the finite-volume
Hamiltonian matrix, but one also learns the composition of the lattice-QCD
eigenstates via the eigenvectors of the Hamiltonian matrix. One learns the
composition of the states in terms of the meson-baryon basis states considered
in formulating the effective field theory. One also learns the composition of
the resonances observed in Nature. In this paper, we will focus on recent
breakthroughs in our understanding of the structure of the $N^*(1535)$,
$N^*(1440)$ and $\Lambda^*(1405)$ resonances using this method.
