Advances in flexible and stretchable electronics have enabled an unprecedented level of coupling between electronics and bio-tissues by overcoming obstacles associated with the bio-tissues' curvilinearity, softness, deformability, and wetness. This review begins by detailing the outstanding challenges in achieving body-conformable electronics stemming from the disparate properties of bio-tissues and man-made materials and the complexity of their interfaces. Given tissue properties, an existing mechanics model has revealed how device softness and interfacial adhesion govern the bio-electronics conformability. Therefore, we first summarize methods for improving the mechanical compliance of electronics through both material engineering and structural design. Then, we discuss strategies to enhance bio-electronics adhesion in both dry and wet environments. We point out that innovative bio-electronics integration procedures also have a significant impact on bio-electronics conformability. We conclude by providing an outlook into future opportunities and proposing a holistic approach to strategizing body-conformable electronics.