Minimally invasive approaches for cancer diagnosis are an integral step in the quest to improve cancer survival. Liquid biopsies such as blood samples are matrices explored to extract valuable information about the tumor and its state through various indicators, such as proteins, peptides, tumor DNA, or circulating tumor cells. Although these markers are scarce, making their isolation and detection in complex matrices challenging, the development in polymer chemistry producing interesting structures, including molecularly imprinted polymers, branched polymers, nanopolymer composites, and hybrids, allowed the development of enhanced platforms with impressive performance for liquid biopsies analysis. This review describes the latest advances and developments in polymer synthesis and their application for minimally invasive cancer diagnosis. The polymer structures improve the operational performances of biosensors through various processes, such as increased affinity for enhanced sensitivity, improved binding, and avoidance of non-specific interactions for enhanced specificity. Furthermore, polymer-based materials can be a tremendous help in signal amplification of usually low-concentrated targets in the sample. The pros and cons of these materials, how the synthesis process affects their performance, and the device applications for liquid biopsies diagnosis will be critically reviewed to show the essentiality of this technology in oncology and clinical biomedicine.