Colorectal cancer (CRC) is the most frequently occurring malignancy in the world. However, the mortality from CRC can be reduced through early diagnostics, selection of the most effective treatment, observation of the therapy success, and the earliest possible diagnosis of recurrences. A comprehensive analysis of genetic and epigenetic factors contributing to the CRC development is needed to refine diagnostic, therapeutic, and preventive strategies and to ensure appropriate decision making in managing specific CRC cases. The liquid biopsy approach utilizing circulating markers has demonstrated its good performance as a tool to detect the changes in the molecular pathways associated with various cancers. In this review, we attempted to brief the main tendencies in the development of circulating DNA and RNA-based markers in CRC such as cancer-associated DNA mutations, DNA methylation changes, and non-coding RNA expression shifts. Attention is devoted to the existing circulating nucleic acid-based CRC markers, the possibility of their application in clinical practice today, and their future improvement. Approaches to the discovery and verification of new markers are described, and the existing problems and potential solutions for them are highlighted.