According to the National Cancer Institute as of April of this year, there is no correlation between smartphone usage and developing brain or nervous system cancer.
Cell phone radiation corresponds to the electromagnetic spectrum's radiofrequency section, giving off amounts of non-ionizing radiation too small to harm human DNA. The only understood effect of radiofrequency waves emitted by cell phones is warming areas of the body in contact with a device.
Notably: the most extensive case-control study ever conducted to examine causation between smartphone use and neck and head tumors presents a possible contradiction.The study's subjects and researchers spanned thirteen countries. It found a positive correlation "between intracranial distribution of tumors within the brain and self-reported location of the phone." However, the study authors asserts that a causal association was indeterminable based on the researchers' discoveries.
Source: https://www.cancer.gov/about-cancer/causes-prevention/risk/radiation/cell-phones-fact-sheet