A large number of proteins are successfully used to treat various diseases. These include natural polypeptide hormones, their synthetic analogues, antibodies, antibody mimetics, enzymes, and other drugs based on them. Many of them are demanded in clinical settings and commercially successful, mainly for cancer treatment. The targets for most of the aforementioned drugs are located at the cell surface. Meanwhile, the vast majority of therapeutic targets, which are usually regulatory macromolecules, are located inside the cell. Traditional low molecular weight drugs freely penetrate all cells, causing side effects in non-target cells. In addition, it is often difficult to elaborate a small molecule that can specifically affect protein interactions. Modern technologies make it possible to obtain proteins capable of interacting with almost any target. However, proteins, like other macromolecules, cannot, as a rule, freely penetrate into the desired cellular compartment. Recent studies allow us to design multifunctional proteins that solve these problems. This review considers the scope of application of such artificial constructs for the targeted delivery of both protein-based and traditional low molecular weight drugs, the obstacles met on the way of their transport to the specified intracellular compartment of the target cells after their systemic bloodstream administration, and the means to overcome those difficulties.