Embodiments are related to the accurate detection of somatic mutations in the plasma (or other samples containing cell-free DNA) of cancer patients and for subjects being screened for cancer. The detection of these molecular markers would be useful for the screening, detection, monitoring, management, and prognostication of cancer patients. For example, a mutational load can be determined from the identified somatic mutations, and the mutational load can be used to screen for any or various types of cancers, where no prior knowledge about a tumor or possible cancer of the subject may be required. Embodiments can be useful for guiding the use of therapies (e.g. targeted therapy, immunotherapy, genome editing, surgery, chemotherapy, embolization therapy, anti-angiogenesis therapy) for cancers. Embodiments are also directed to identifying de novo mutations in a fetus by analyzing a maternal sample having cell-free DNA from the fetus.