Molecular motors are protein nanomachines that organize the internal order of all eukaryotic cells by shuttling intracellular cargos. Kinesins, dyneins, and myosins are three identified superfamilies of molecular motors which often function together within the cells. All of these motors power cellular motility using energy derived from adenosine triphosphate (ATP) hydrolysis. Molecular biology has revealed that the functional impairments of molecular motors would contribute to various human diseases, such as Alzheimer and cancer. Engineering developments have also emerged regarding the utilization of molecular motors in nanorobotics with a variety of missions, such as molecular communications. Despite this progress, the properties of intracellular cargo transport are not well understood. Motivated by the recent experimental findings, this thesis proposes computational and mathematical frameworks to investigate two different modes of intracellular cargo transport driven by (i) a single motor and by (ii) an assembly of two coupled identical motors. We focus on the cargo transport by kinesins because kinesin stepping kinetic scheme has been developed previously, and recent experiments have further measured input parameters for our theory. Nevertheless, our models are rather general and can be applied to other types of cytoskeletal molecular motors.