Fabrication of heterostructures using two-dimensional (2D) materials with different bandgaps creates opportunities for exploring new properties and device applications. Ruddlesden-Popper (RP) layered halide perovskites have recently emerged as a new class of solution-processable 2D materials that demonstrate exotic optoelectronic properties. However, heterostructures using 2D halide perovskites have not been achieved. Here, we report a simple solution growth method for making vertically stacked double heterostructures and complex multilayer heterostructures of 2D lead iodide perovskites [(PEA)(2)(MA)(n-1)PbnI3n+1, PEA = C6H5(CH2)(2)NH3+, MA = CH3NH3+] via van der Waals epitaxy. These heterostructures present atomically sharp interfaces and display distinct photoluminescence that allow fingerprinting the RP phases. Time resolved photoluminescence measurements reveal internal energy transfer from higher energy bandgap (lower n value) perovskite layers to lower energy bandgap (higher n value) perovskite layers on the time scale of hundreds of picoseconds due to natural type I band alignments. These results offer new strategies to fabricate perovskite-perovskite heterojunctions by taking advantage of surface-bound ligands as spatial barriers to prevent ion migration across the junctions. These heterostructures capable of multicolor emission with high spectral purity are promising for light-emitting applications.