Directed self-assembly (DSA) of block copolymers (BCP) can multiply the resolution of conventional lithography and has been studied extensively for the next generation of nanopatterning. Great progress has been made in DSA using guide patterns with chemical or topographical contrast to achieve high levels of ordering, registration and pattern complexity. However, most of the focus has been on perfecting the two-dimensional ordering of BCP for pattern transfer and the investigation on the three-dimensional (3D) structures inside the BCP films has been rare. Characterization of the 3D structures plays a critical role in understanding the fundamental physics behind polymer assembly and the ability to control the 3D structures offers great potential for direct 3D nanofabrication. This dissertation focuses on the characterization and manipulation of the 3D structures in BCP DSA. In Chapter 1, important literatures and the rationale for studying the 3D structures in DSA are briefly discussed. Chapter 2 describes the membrane sample fabrication method necessary to enable 3D metrologies. The method does not introduce any artifacts or damage to the polymer as DSA is performed prior to back-etched membrane formation. In Chapter 3, we used TEM tomography to systematically and quantitatively investigate the BCP morphology through the film thickness for different template geometries. Results showed that incommensurate confinement from template topography could cause roughness and intermittent dislocations at the bottom of the film. We also demonstrated that the positional fluctuations of the BCP interface between domains showed a depth-dependent behavior. In Chapter 4, we investigated the kinetic evolution of 3D structures in density multiplication DSA. We identified the key 3D transient morphologies and demonstrated that by engineering the DSA conditions to disfavor undesirable metastable structures the speed of assembly could be greatly enhanced. Chapter 5 explores the DSA of 3D structures using 2D chemical patterns. Using sphere-forming BCP, we showed that the crystallographic symmetries and orientations of the 3D lattice could be deliberately controlled and the ordered structure is able to propagate through 300 nm thick films. We also estimated the relative stability of different crystallographic geometries and established the rules governing 3D DSA.