We develop and apply a relativistic and non-perturbative approach to bound states and their properties on the light front in Quantum Chromodynamics (QCD). We investigate a Hamiltonian, derived in part from QCD, which features strongly interacting and confined quarks and apply it to heavy flavored mesons. This effective Hamiltonian is developed based on the light-front holographic QCD and an effective one-gluon-exchange interaction. We solve for the mass eigenstates and light-front wave functions (LFWFs) of this effective Hamiltonian using basis light-front quantization (BLFQ). This effective Hamiltonian was first implemented in the heavy quarkonium system where it provided a successful description of the mass spectrum and other physical observables. In this thesis, we will show that, with the least parameter fitting, we can also produce reasonable results for the unequal-mass heavy flavored mesons: $B_c$, $B$, $B_s$, $D$, and $D_s$. In particular, we calculated the mass spectra and corresponding light-front wave functions, illustrate their asymmetric features and employ them to calculate properties of experimental interest such as parton distribution amplitudes and functions.

We further investigate the semileptonic decays of $B_c$ to charmonium. Since the gauge boson involved in the semileptonic decay needs to be in the timelike region, the conventional choice of frame, the Drell-Yan frame, is not suitable for these decays. Instead we adopt a general frame to tackle the kinematics. Due to the complex structure of the hadron current matrix that governs these decays, we employ more than one current component and LFWFs at different magnetic projections. There we also show the frame dependence that is due to the Fock sector truncation, that is our limited treatment of the mesons as quark - antiquark bound states omitting other possible contributions such as gluon excitations.

We also report the dependence of calculated observables on parameters of the basis space, which we show how to minimize.

As a further application of this approach, we apply it to the physical electron system in Quantum Electrodynamics (QED), which is treated as a relativistic electron which can emit and absorb a photon on the light front. We calculate the electromagnetic form factors and gravitational form factors of an electron, and compare our results with the light-front perturbation theory. This work provides insights into the challenges and promise of applying this light-front Hamiltonian approach to more complete treatments of QCD in the future.