Targeted drug delivery into the cell compartment that is the most vulnerable to effects of the corresponding drug is a challenging problem, and its successful solution can significantly increase the efficiency and reduce side effects of the delivered therapeutic agents. To accomplish this one can utilize natural mechanisms of cellular specific uptake of macromolecules by receptor-mediated endocytosis and intracellular transport between cellular compartments. A transporting construction combining the components responsible for different steps of intracellular transport is promising for creating multifunctional modular constructions capable of delivering the necessary therapeutic agent into a given compartment of type-specified cells. This review focuses on intracellular transport peculiarities along with approaches for designing such transporting constructions for new, more effective, and safer strategies for treatment of various diseases.