Transfer printing is becoming widely adopted as a back-end process for the hybrid integration of photonic and electronic devices. Integration of membrane components, with micrometer-scale footprints and sub-micron waveguide dimensions, imposes strict performance requirements on the process. In this review, we present an overview of transfer printing for integrated photonics applications, covering materials and fabrication process considerations, methods for efficient optical coupling, and high-accuracy inter-layer alignment. We present state-of-the-art integration demonstrations covering optical sources and detectors, quantum emitters, sensors, and opto-mechanical devices. Finally, we look toward future developments in the technology that will be required for dense multi-materials integration at wafer scales.