Global health and food security constantly face the challenge of emerging human and plant diseases caused by bacteria, viruses, fungi, and other pathogens. Disease outbreaks such as SARS, MERS, Swine Flu, Ebola, and COVID-19 (on-going) have caused suffering, death, and economic losses worldwide. To prevent the spread of disease and protect human populations, rapid point-of-care (POC) molecular diagnosis of human and plant diseases play an increasingly crucial role. Nucleic acid-based molecular diagnosis reveals valuable information at the genomic level about the identity of the disease-causing pathogens and their pathogenesis, which help researchers, healthcare professionals, and patients to detect the presence of pathogens, track the spread of disease, and guide treatment more efficiently. A typical nucleic acid-based diagnostic test consists of three major steps: nucleic acid extraction, amplification, and amplicon detection. Among these steps, nucleic acid extraction is the first step of sample preparation, which remains one of the main challenges when converting laboratory molecular assays into POC tests. Sample preparation from human and plant specimens is a time-consuming and multi-step process, which requires well-equipped laboratories and skilled lab personnel. To perform rapid molecular diagnosis in resource-limited settings, simpler and instrument-free nucleic acid extraction techniques are required to improve the speed of field detection with minimal human intervention. This review summarizes the recent advances in POC nucleic acid extraction technologies. In particular, this review focuses on novel devices or methods that have demonstrated applicability and robustness for the isolation of high-quality nucleic acid from complex raw samples, such as human blood, saliva, sputum, nasal swabs, urine, and plant tissues. The integration of these rapid nucleic acid preparation methods with miniaturized assay and sensor technologies would pave the road for the "sample-in-result-out" diagnosis of human and plant diseases, especially in remote or resource-limited settings.