Liquid biopsies that analyze cell-free DNA in blood plasma are used for noninvasive prenatal testing, oncology, and monitoring of organ transplant recipients. DNA molecules are released into the plasma from various bodily tissues. Physical and molecular features of cell-free DNA fragments and their distribution over the genome bear information about their tissues of origin. Moreover, patterns of DNA methylation of these molecules reflect those of their tissue sources. The nucleosomal organization and nuclease content of the tissue of origin affect the fragmentation profile of plasma DNA molecules, such as fragment size and end motifs. Besides double-stranded linear fragments, other topological forms of cell-free DNA also exist-namely circular and single-stranded molecules. Enhanced by these features, liquid biopsies hold promise for the noninvasive detection of tissue-specific pathologies with a range of clinical applications.