Biological systems are mechanically soft, with complex, time-dependent 3D curvilinear shapes; modern electronic and microfluidic technologies are rigid, with simple, static 2D layouts. Eliminating this profound mismatch in physical properties will create vast opportunities in man-made systems that can intimately integrate with the human body, for diagnostic, therapeutic or surgical function with important, unique capabilities in fitness/wellness, sports performance and clinical healthcare. Over the last decade, a convergence of new concepts in materials science, mechanical engineering, electrical engineering and advanced manufacturing has led to the emergence of diverse classes of 'biocompatible' electronic and microfluidic systems. This talk will describe the key ideas and present some of the most recent device examples, including wireless, battery-free electronic 'tattoos' with applications in continuous monitoring of vital signs in maternal, fetal, neonatal and pediatric care; and microfluidic/electronic platforms that can capture, manipulate and perform biomarker analysis on microliter volumes of sweat, with applications in medical diagnostics and sports performance.