Over the past few decades, numerous polymer drug carrier systems are designed and synthesized, and their properties are evaluated. Many of these systems are based on water‐soluble polymer carriers of low‐molecular‐weight drugs and compounds, e.g., cytostatic agents, anti‐inflammatory drugs, or multidrug resistance inhibitors, all covalently bound to a carrier by a biodegradable spacer that enables controlled release of the active molecule to achieve the desired pharmacological effect. Among others, the synthetic polymer carriers based on N‐(2‐hydroxypropyl) methacrylamide (HPMA) copolymers are some of the most promising carriers for this purpose. This review focuses on advances in the development of HPMA copolymer carriers and their conjugates with anticancer drugs, with triggered drug activation in tumor tissue and especially in tumor cells. Specifically, this review highlights the improvements in polymer drug carrier design with respect to the structure of a spacer to influence controlled drug release and activation, and its impact on the drug pharmacokinetics, enhanced tumor uptake, cellular trafficking, and in vivo antitumor activity.