Self-assembly refers to a process in which initially disordered systems spontaneously form ordered structures over time driven by the interactions between the building blocks. The self-assembly of soft materials systems, such as colloids and peptides, has drawn a lot of research interest. When their components and intermolecular interactions are carefully calibrated, these systems could self-assemble into interesting nanostructures with practical applications, such as colloidal crystalline lattices or peptide nanorods. A major area of study in self-assembly is then the rational design of the building blocks and interactions between them to direct these systems to self-assemble into target nanostructures. This is the so-called "inverse design" problem, where we are given a target nanostructure and would like to figure out the optimal building block and interactions that could lead to the target structure. In our works, we explore and develop various inverse design techniques for anisotropic colloids and peptides. We begin by employing molecular simulation techniques, such as molecular dynamics and Monte Carlo simulations, to characterize the ability of a particular building block design to form the target structure. Then we use modern optimization and machine learning algorithms to find the optimal design that could lead to maximum ability to form the target structure. Based on this general methodology, we have developed (1) inverse design protocols that optimize anisotropic colloids to self-assemble into target crystalline lattices with omnidirectional optical bandgaps by combining molecular simulation with stochastic optimization algorithm and (2) high-throughput screening pipeline to find optimal peptides that could self-assemble into vesicular structures as chassis materials for synthetic cells using molecular simulation and Bayesian optimization.