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Deep implicit functions have shown remarkable shape modeling ability in various 3D computer vision tasks. One drawback is that it is hard for them to represent a 3D shape as multiple parts. Current solutions learn various primitives and blend the primitives directly in the spatial space, which still struggle to approximate the 3D shape accurately. To resolve this problem, we introduce a novel implicit representation to represent a single 3D shape as a set of parts in the latent space, towards both highly accurate and plausibly interpretable shape modeling. Our insight here is that both the part learning and the part blending can be conducted much easier in the latent space than in the spatial space. We name our method Latent Partition Implicit (LPI), because of its ability of casting the global shape modeling into multiple local part modeling, which partitions the global shape unity. LPI represents a shape as Signed Distance Functions (SDFs) using surface codes. Each surface code is a latent code representing a part whose center is on the surface, which enables us to flexibly employ intrinsic attributes of shapes or additional surface properties. Eventually, LPI can reconstruct both the shape and the parts on the shape, both of which are plausible meshes. LPI is a multi-level representation, which can partition a shape into different numbers of parts after training. LPI can be learned without ground truth signed distances, point normals or any supervision for part partition. LPI outperforms the latest methods under the widely used benchmarks in terms of reconstruction accuracy and modeling interpretability. Our code, data and models are available at https://github.com/chenchao15/LPI.