Recently, the integration of electronic elements with cellular scaffolds has brought forth the ability to monitor and control tissue function actively by using flexible free-standing two-dimensional (2D) systems. Capabilities for electrically probing complex, physicochemical and biological three-dimensional (3D) microenvironments demand, however, 3D electronic scaffolds with well-controlled geometries and functional-component distributions. This work presents the development of flexible 3D electronic scaffolds with precisely defined dimensions and microelectrode configurations formed using a process that relies on geometric transformation of 2D precursors by compressive buckling. It demonstrates a capability to fabricate these constructs in diverse 3D architectures and/or electrode distributions aimed at achieving an enhanced level of control and regulation of tissue function relatively to that of other approaches. In addition, this work presents the integration of these 3D electronic scaffolds within engineered 3D cardiac tissues, for monitoring of tissue function, controlling tissue contraction through electrical stimulation, and initiating on-demand, local release of drugs, each through well-defined volumetric spaces. These ideas provide opportunities in fields ranging from in vitro drug development to in vivo tissue repair and many others.