There is a strong desire for novel chemical sensors that can detect low concentrations of volatile organic compounds (VOCs) for early-stage disease diagnostics as well as various environmental monitoring applications. The aim of this thesis work was to address these challenges by developing an “electronic nose” (e-nose) platform based on chemical sensor arrays capable of detecting and differentiating between various VOCs of interest. Sensor arrays were fabricated in a field-effect transistor (FET) configuration with exquisitely sensitive carbon nanotubes (CNTs) as the channel material. The nanotubes were functionalized with a variety of single-stranded DNA oligomers, forming DNA-NT hybrid structures with affinity to a wide variety of VOC targets. Interactions between DNA-NTs and VOCs yielded changes in sensor conductivity that depended strongly on the base sequence of DNA. Arrays of CNT devices were functionalized with up to ten different DNA oligomers to enable electronic signature readouts of VOC binding events. DNA-NT responses were processed with pattern recognition algorithms in order to classify different VOC targets according to their chemical “fingerprints.” This technology was used to measure VOC biomarkers associated with ovarian cancer and COVID-19 from human fluid media. DNA-NT arrays measured headspaces VOCs from 58 blood plasma samples from individual people, including 15 with a late-stage malignant form of ovarian cancer, 6 with early-stage malignant cancer, 16 with a benign form of cancer, and 21 healthy age-matched controls. Statistical techniques based on machine learning were used to discriminate between the malignant, benign, and healthy groups with 90 – 95% classification accuracy. Furthermore, all six early-stage samples were correctly identified with the malignant group, indicating significant progress towards an effective screening method for ovarian cancer. Similar investigations were conducted on sweat samples procured from patients who had tested positive for COVID-19 (CoV+) and those who had tested negative (CoV-). Statistical analysis of the DNA-NT responses to the sweat headspace VOCs revealed highly differentiated clusters associated with the CoV+ and CoV- groups. A binary classifier was constructed using the response data and was estimated to have a 99% classification success rate, suggesting strong potential for utilizing DNA-NTs for COVID screening. Finally, DNA-NT arrays were assessed based on various performance characteristics desired for remote environmental monitoring applications such as pollution monitoring and explosives detection in a warzone. A series of experiments was conducted to evaluate DNA-NT sensitivity, specificity, and longevity using mixtures of 2,6-dinitrotoluene (DNT) and dimethyl methylphosphonate (DMMP) to simulate complex VOC environments. The sensors demonstrated sensitivity to parts-per-billion concentrations of DNT in a highly concentrated background of DMMP. Moreover, the shelf life of these sensors was projected on the order of months, making DNA-NTs promising candidates for a wide range of applications.