Photodetectors (PDs) used in communication systems require ultrafast response, high efficiency, and low noise. PDs with such characteristics are increasingly in demand for data centers, metro data links, and long-haul optical networks. In a surface-illuminated PD, high speed and high efficiency are often a tradeoff, since a high-speed device needs a thin absorption layer to reduce the carrier transit time, whereas a high-efficiency device needs a thick absorption layer to compensate for the low absorption coefficient of some semiconductors such as Si and Germanium (Ge) or SiGe alloys at wavelengths near the bandgap. In this part of this review, we present the recent efforts in enhancing the photon–material interactions by using low-dimensional structures that can control light for more interaction with the photoabsorbing materials, slow down the propagation group velocity and reduce surface reflection. We present recent demonstrations of high-speed PDs based on nanostructures enabled by both synthetic bottom-up or transformative top-down processing methods. In particular, we detail a CMOS-compatible ultrafast surface-illuminated Si PD with 30-ps full-width at half-maximum, and >50% efficiency at 850 nm. A complementary discussion on device challenges and the integration of low-dimensional structures will be presented in the part II of this review.