A significant part of developing new materials is understanding the relations between their component elements, microstructures and macroscale physical and chemical properties, which in turn determine their use in various industries such as construction, automobile, or biomaterials. Historically, such characterization was done mainly by laboratory experiments, whereas in recent times, computational models and high-fidelity simulations have made the process more efficient. However, improving the reliability of simulations is still dependent on measures like using finer meshes, smaller time steps, larger length scales and time scales which, together, can lead to exponential increase in the computational time and cost. Moreover, material characterization often requires high-throughput analyses, where such expensive simulations need to be repeated thousands of times, making the study prohibitively costly. As an alternative, data driven techniques in the form of surrogate models show great promise for accelerated material discovery. This dissertation identifies major advantages of using machine learning (ML) algorithms in materials research via three studies that focus on using ML for fast evaluation of structure-property relations, discovery of unique toughening mechanisms and optimizing microstructural designs, respectively. The first study explores the usefulness of various ML algorithms to learn from molecular dynamics (MD) simulations and decode structure-property relations of 2D nanomaterials. It also analyzes the sensitivity of performance of these algorithms to the form of microstructure description, ranging from raw forms such as atomic coordinates to tailor-made low dimensional representations. It shows that certain surrogate models are able to predict useful macroscale properties by analyzing raw forms of the microstructure with minimum pre-processing. It also demonstrates that significant computational costs can be saved by re-using models trained on one 2D material (boron nitride) to predict properties of another 2D material (graphite) via transfer learning. The surrogate models trained in this study predicted the MD results with over 95% accuracy while training on just 10% of data from the simulations. While this study demonstrates the computational advantage in using ML models for analysis, the subsequent study uses such fast analyses for designing advantageous materials. The focus of the second study is on using surrogate model-based analyses to design multi-scale hierarchical checkerboard composites, in which, the macroscopic properties are influenced by microstructures at multiple hierarchies. It shows that in such complicated cases, it is inadequate to train one surrogate model for structure-property predictions and designs a strategy in which many surrogate agents with specific narrowed objectives work with each other to form teams. These teams ultimately predict the material behavior with high accuracy, offering inexpensive yet accurate evaluations of the composites. The surrogates are then used to exhaustively explore the design space and discover near-optimal structural designs to maximize the macroscopic toughness for a wide variety of base materials. The study uncovers various toughening mechanisms in composites that are uniquely applicable to specific types of base materials. Finite element simulations and tensile experiments conducted on 3D printed specimens validate the toughening mechanisms discovered by the surrogate agents. Finally, the third study focuses on the use of ML algorithms for optimizing composite structures without using surrogate models. It introduces a new topology optimization procedure that uses generative adversarial neural networks (GAN) in the genetic algorithm (GA) iterations to result in better exploration of near-optimal topologies. When compared with traditional GA, the proposed algorithm, GAN-GA, is found to consistently identify a greater number of near-optimal solutions while needing to evaluate a lesser number of candidates.