Thin-film transistors (TFTs) and circuits based on oxide semiconductors fabricated on flexible plastic foils and stretchable substrates are reported. Reliable fabrication protocols, using InGaZnO as n-type semiconductor, in combination with different design strategies, aiming at the improvement of both the electrical performance and the mechanical stability of such electronics, are discussed. First, simulation models are used to guide the fabrication of operational amplifiers and logic circuits on flexible polyimide foil, using an additional third metal layer for the interconnections. Thanks to the reduced parasitic resistances and capacitances, the resulting circuits have yielded improved electrical performances with respect to a two-metals architecture. In particular, an increase of 5.7% of the Gain-Bandwidth-Product (GBWP) for operational amplifiers, and an average reduction of 22% of the rise times, fall times and propagation delays for digital circuits, were achieved. In parallel, Finite-Element Modeling (FEM) has supported the design of engineered stretchable substrates shaped with pillar (or mesa) structures. The reduction of the strain experienced by the electronics, located on the mesa surfaces, during stretching, bending, and twisting, resulted in highly flexible digital circuits with functionality up to 20% elongation.