This dissertation addresses challenges pertaining to multi-junction (MJ) solar cells from material development to device design and characterization. Firstly, among the various methods to improve the energy conversion efficiency of MJ solar cells using, a novel approach proposed recently is to use II-VI (MgZnCd)(SeTe) and III-V (AlGaIn)(AsSb) semiconductors lattice-matched on GaSb or InAs substrates for current-matched subcells with minimal defect densities. CdSe/CdTe superlattices are proposed as a potential candidate for a subcell in the MJ solar cell designs using this material system, and therefore the material properties of the superlattices are studied. The high structural qualities of the superlattices are obtained from high resolution X-ray diffraction measurements and cross-sectional transmission electron microscopy images. The effective bandgap energies of the superlattices obtained from the photoluminescence (PL) measurements vary with the layer thicknesses, and are smaller than the bandgap energies of either the constituent material. Furthermore, The PL peak position measured at the steady state exhibits a blue shift that increases with the excess carrier concentration. These results confirm a strong type-II band edge alignment between CdSe and CdTe. The valence band offset between unstrained CdSe and CdTe is determined as 0.63 eV±0.06 eV by fitting the measured PL peak positions using the Kronig-Penney model. The blue shift in PL peak position is found to be primarily caused by the band bending effect based on self-consistent solutions of the Schrödinger and Poisson equations. Secondly, the design of the contact grid layout is studied to maximize the power output and energy conversion efficiency for concentrator solar cells. Because the conventional minimum power loss method used for the contact design is not accurate in determining the series resistance loss, a method of using a distributed series resistance model to maximize the power output is proposed for the contact design. It is found that the junction recombination loss in addition to the series resistance loss and shadowing loss can significantly affect the contact layout. The optimal finger spacing and maximum efficiency calculated by the two methods are close, and the differences are dependent on the series resistance and saturation currents of solar cells. Lastly, the accurate measurements of external quantum efficiency (EQE) are important for the design and development of MJ solar cells. However, the electrical and optical couplings between the subcells have caused EQE measurement artifacts. In order to interpret the measurement artifacts, DC and small signal models are built for the bias condition and the scan of chopped monochromatic light in the EQE measurements. Characterization methods are developed for the device parameters used in the models. The EQE measurement artifacts are found to be caused by the shunt and luminescence coupling effects, and can be minimized using proper voltage and light biases. Novel measurement methods using a pulse voltage bias or a pulse light bias are invented to eliminate the EQE measurement artifacts. These measurement methods are nondestructive and easy to implement. The pulse voltage bias or pulse light bias is superimposed on the conventional DC voltage and light biases, in order to control the operating points of the subcells and counterbalance the effects of shunt and luminescence coupling. The methods are demonstrated for the first time to effectively eliminate the measurement artifacts.