Recently, numerous polymer materials have been employed as drug carrier systems in medicinal research, and their detailed properties have been thoroughly evaluated. Water-soluble polymer carriers play a significant role between these studied polymer systems as they are advantageously applied as carriers of low-molecular-weight drugs and compounds, e.g., cytostatic agents, anti-inflammatory drugs, antimicrobial molecules, or multidrug resistance inhibitors. Covalent attachment of carried molecules using a biodegradable spacer is strongly preferred, as such design ensures the controlled release of the drug in the place of a desired pharmacological effect in a reasonable time-dependent manner. Importantly, the synthetic polymer biomaterials based on -(2-hydroxypropyl) methacrylamide (HPMA) copolymers are recognized drug carriers with unique properties that nominate them among the most serious nanomedicines candidates for human clinical trials. This review focuses on advances in the development of HPMA copolymer-based nanomedicines within the passive and active targeting into the place of desired pharmacological effect, tumors, inflammation or bacterial infection sites. Specifically, this review highlights the safety issues of HPMA polymer-based drug carriers concerning the structure of nanomedicines. The main impact consists of the improvement of targeting ability, especially concerning the enhanced and permeability retention (EPR) effect.