Explosive growth in demand for data traffic has prompted exploration of the spatial dimension of light waves, which provides a degree of freedom to expand data transmission capacity. Various techniques based on bulky optical devices have been proposed to tailor light waves in the spatial dimension. However, their inherent large size, extra loss, and precise alignment requirements make these techniques relatively difficult to implement in a compact and flexible way. In contrast, three-dimensional (3D) photonic chips with compact size and low loss provide a promising miniaturized candidate for tailoring light in the spatial dimension. Significantly, they are attractive for chip-assisted short-distance spatial mode optical interconnects that are challenging to bulky optics. Here, we propose and fabricate femtosecond laser-inscribed 3D photonic chips to tailor orbital angular momentum (OAM) modes in the spatial dimension. Various functions on the platform of 3D photonic chips are experimentally demonstrated, including the generation, (de)multiplexing, and exchange of OAM modes. Moreover, chip-chip and chip–fiber–chip short-distance optical interconnects using OAM modes are demonstrated in the experiment with favorable performance. This work paves the way to flexibly tailor light waves on 3D photonic chips and offers a compact solution for versatile optical interconnects and other emerging applications with spatial modes.