Capabilities for non-invasive measurement of neural signals are important because they support many critical biomedical applications, including brain-machine interface paradigms in mobile applications. Currently, recording neural signals in mobile environments is a challenge because conventional measurement devices have rigid or mildly flexible construction and bulky cables for signal conduction. Technologies of the future must address these drawbacks, through new ideas that provide ultrathin, conformal designs, with high fidelity and non-invasive measurement modes. Our research group, in conjunction with the research group of John Rogers at UIUC, is developing foldable, stretchable electrode arrays that can non-invasively measure neural signals (i.e. EEG) without the need for gel. The electrodes rely on layouts recently developed for silicon electronics that offer linear elastic responses to applied force, with the capacity to fold, twist and deform into various curved shapes. Stretchable electronics have the key advantage that they can wrap arbitrary, curvilinear surfaces and, at the same time, achieve mechanical properties that approach those of tissues of the human body (e.g. skin). These capabilities are especially significant for applications in skin-mounted devices for electroencephalography (EEG) in mobile environments.