Skin-mounted epidermal electronics, a strategy for bio-integrated electronics, provide an avenue to non-invasive monitoring of clinically relevant physiological signals for healthcare applications. Current conventional systems consist of single-point sensors fastened to the skin with adhesives, and sometimes with conducting gels, which limits their use outside of clinical settings due to loss of adhesion and irritation to the user. In order to facilitate extended use of skin-mounted healthcare sensors without disrupting everyday life, we envision electronic monitoring systems that integrate seamlessly with the skin below the notice of the user. This manuscript reviews recent significant results towards our goal of wearable electronic sensor systems for long-term monitoring of physiological signals. Ultra-thin epidermal electronic systems (EES) are demonstrated for extended use on the skin, in a conformal manner, including during everyday bathing and sleeping activities. We describe the assessment of clinically relevant physiological parameters, such as electrocardiograms (ECG), electromyograms (EMG), electroencephalograms (EEG), temperature, mechanical strain and thermal conductivity, using examples of multifunctional EES devices. Additionally, we demonstrate capability for real life application of EES by monitoring the system functionality, which has no discernible change, during cyclic fatigue testing.