Two-dimensional (2D) materials have attracted broad interests and been extensively exploited for a variety of functional applications. Moreover, one-dimensional (1D) atomic crystals can also be integrated into 2D templates to create mixed-dimensional heterostructures, and the versatility of combinations provides 2D-1D heterostructures plenty of intriguing physical properties, making them promising candidate to construct novel electronic and optoelectronic nanodevices. In this review, we first briefly present an introduction of relevant fabrication methods and structural configurations for 2D-1D heterostructures integration. We then discuss the emerged intriguing physics, including high optical absorption, efficient carrier separation, fast charge transfer and plasmon-exciton interconversion. Their potential applications such as electronic/optoelectronic devices, photonic devices, spintronic devices and gas sensors, are also discussed. Finally, we provide a brief perspective for the future opportunities and challenges in this emerging field.