Conventional integrated photonic devices are fabricated on rigid semiconductor or dielectric substrates and are therefore inherently incompatible with soft biological tissues. Over the past few years, we have developed a suite of active and passive photonic devices and systems integrated on plastic substrates which can be bent, twisted, and stretched without compromising their optical performance. In this talk, we will review the latest progress in multi-material photonic integration on unconventional flexible substrates, and discuss emerging applications of flexible photonics in biological sensing and high-bandwidth data communications.