Lattice structures are attractive lightweight structures with superior properties, such as high specific stiffness and strength, energy absorption, vibration reduction, structural stability, and heat dissipation. They are widely used across various engineering fields, including automotive, aerospace, and biomedical engineering. Topology optimization, an efficient design tool, holds significant potential for optimizing the topologies of lattice microstructures and the macrostructure. This thesis focuses on the design of lattice structures while addressing the challenges in conventional multi-scale topology optimization approaches, such as limited design space, extensive computational cost, and connectivity issues between dissimilar lattice microstructures. Firstly, a concurrent multi-scale multi-material topology optimization method for designing lattice structures composed of solid microstructures and multiple types of lattice microstructures is presented. This method uses a multi-material topology optimization algorithm to achieve the optimal distribution of microstructures, balancing the design space with the computational cost. A new gradient-controlled method is proposed to identify the interface layers between dissimilar lattice microstructures and fill them with solid materials to ensure connectivity. In this approach, the topology of the macrostructure, and the topologies and distributions of microstructures, are simultaneously optimized. Secondly, a concurrent multi-scale multi-joint topology optimization method for designing lattice structures comprising multiple types of lattice microstructures is proposed. This method considers multiple types of designable interface microstructures (referred to as joints) to expand the design space, with each joint containing a non-designable frame domain to satisfy connectivity requirements. In addition to the topology of the macrostructure and the topologies and distributions of lattice microstructures, the topologies of interface microstructures and their locations within interface domains are simultaneously optimized. Lastly, a concurrent multi-scale topology optimization method that considers fiber orientation is established. Unlike previous studies, which restricted the base material to the isotropic domain, this research considers anisotropic fiber-reinforced composites and incorporates fiber orientation optimization into the design of multi-scale lattice structures. The proposed method demonstrates substantial performance enhancements, achieving compliance improvements of 13%, 26%, and 61% across three numerical examples that feature three lattice microstructures, compared with designs using the conventional multi-scale topology optimization method which does not account for fiber orientation optimization.