The development of integrated optical circuits has enabled a diverse portfolio of chipscale photonic applications—ranging from data communication over sensing to imaging—that is set to grow further as new device concepts in, for example, quantum information processing and optical neural networks mature. While silicon photonics has emerged as a viable candidate to translate proof-of-principle demonstrations to mass-manufacturing, the fabrication of photonic integrated circuits (PICs) and their subcomponents remains highly heterogeneous, which drives up cost and slows down progress towards faster and more power-efficient performance. In this dissertation, I demonstrate how single-layer graphene (SLG) can bring active functionality to arbitrary passive waveguide platforms, offering a more universal approach to developing integrated photonic components. SLG can be transferred to PICs without the limitations or complexity of traditional deposition or bonding processes. It also stands to outperform conventional semiconductors in terms of speed and spectral operating range due to its ultra-fast carrier dynamics, high carrier mobility, and gapless bandstructure. Using the key component for optical-to-electrical signal conversion—the photodetector—as an example, here I demonstrate graphene-based components on three different PIC platforms. First, I show plasmonic enhanced graphene photodetectors (GPDs) on silicon nitride waveguides, which generate a voltage from optically generated hot-carrier distributions in SLG via the photo-thermoelectric (PTE) effect. Then, I demonstrate PTE-GPDs—fabricated from layered material heterostructures—on a silicon-on-insulator microring resonator. Both detectors operate at Telecom wavelengths (λ = 1.55 μm), are compatible with high-speed (> 10 GHz) operations, and hold the current records in voltage responsivity—R ∼ 12 V/W and R ∼ 90 V/W—for waveguide-integrated GPDs fabricated from chemical vapour deposited and mechanically exfoliated SLG, respectively. I then go on to show how established GPD concepts can be translated to an integrated mid-infrared (λ = 3.8 μm) platform based on sub-wavelength grating waveguides in silicon and study how light-graphene interaction under in-plane incidence can be further optimised to improve GPD performance. Finally, I develop new approaches towards high-quality, scalable SLG on PICs, critically required to advance graphene-based integrated photonics towards industrial production.