We present a technique for parsing widely used furniture assembly instructions, and reconstructing the 3D models of furniture components and their dynamic assembly process. Our technique takes as input a multi-step assembly instruction in a vector graphic format and starts to group the vector graphic primitives into semantic elements representing individual furniture parts, mechanical connectors (e.g., screws, bolts and hinges), arrows, visual highlights, and numbers. To reconstruct the dynamic assembly process depicted over multiple steps, our system identifies previously built 3D furniture components when parsing a new step, and uses them to address the challenge of occlusions while generating new 3D components incrementally. With a wide range of examples covering a variety of furniture types, we demonstrate the use of our system to animate the 3D furniture assembly process and, beyond that, the semantic-aware furniture editing as well as the fabrication of personalized furnitures.