In human exhaled breath, more than 3000 volatile organic compounds (VOCs) are found, which are directly or indirectly related to internal biochemical processes in the body. Electronic noses (E-noses) could play a potential role in screening/analyzing various respiratory and systemic diseases by studying breath signatures. An E-nose integrates a sensor array and an artificial neural network that responds to specific patterns of VOCs, and thus can act as a non-invasive technology for disease monitoring. The gold standard blood glucose monitoring test for diabetes diagnostics is invasive and highly uncomfortable. This contributes to the massive need for technologies which are non-invasive and can be used as an alternative to blood measurements for glucose detection. While lung cancer is one of the deadliest cancers with the highest death rate and an extremely high yearly global burden, the conventional diagnosis means, such as sputum cytology, chest radiography, or computed tomography, do not support wide-range population screening. A few standard non-invasive techniques, such as mass spectrometry and gas chromatography, are expensive, non-portable, and require skilled personnel for operation and are again not suitable for large-scale screening. Breath contains markers for both diabetes and lung cancer along with markers for several diseases and thus, a non-invasive technique such as the E-nose would greatly improve analysis procedures over existing invasive methods. This review shows the state-of-the-art technologies for VOC detection and machine learning approaches for two clinical models: diabetes and lung cancer detection.