With the intense interest in inorganic cesium lead halide perovskites and their nanostructures for optoelectronic applications, high-quality crystalline nanomaterials with controllable morphologies and growth directions are desirable. Here, we report a vapor-phase epitaxial growth of horizontal single-crystal CsPbX3 (X = Cl, Br, I) nanowires (NWs) and microwires (MWs) with controlled crystallographic orientations on the (001) plane of phlogopite and muscovite mica. Moreover, single NWs, Y-shaped branches, interconnected NW or MW networks with 6-fold symmetry, and, eventually, highly dense epitaxial network of CsPbBr3 with nearly continuous coverage were controllably obtained by varying the growth time. Detailed structural study revealed that the CsPbBr3 wires grow along the [001] directions and have the (100) facets exposed. The incommensurate heteroepitaxial lattice match between the CsPbBr3 and mica crystal structures and the growth mechanism of these horizontal wires due to asymmetric lattice mismatch were proposed. Furthermore, the photoluminescence waveguiding and good performance from the photodetector device fabricated with these CsPbBr3 networks demonstrated that these well-connected CsPbBr3 NWs could serve as straightforward platforms for fundamental studies and optoelectronic applications.