Systems, methods, and apparatuses can determine and use methylation profiles of various tissues and samples. Examples are provided. A methylation profile can be deduced for fetal/tumor tissue based on a comparison of plasma methylation (or other sample with cell-free DNA) to a methylation profile of the mother/patient. A methylation profile can be determined for fetal/tumor tissue using tissue-specific alleles to identify DNA from the fetus/tumor when the sample has a mixture of DNA. A methylation profile can be used to determine copy number variations in genome of a fetus/tumor. Methylation markers for a fetus have been identified via various techniques. The methylation profile can be determined by determining a size parameter of a size distribution of DNA fragments, where reference values for the size parameter can be used to determine methylation levels. Additionally, a methylation level can be used to determine a level of cancer.