The increasing penetration of proactive agents in distribution systems (DS) has opened new possibilities to make the grid more resilient and to increase participation of responsive loads (RL) and non-conventional generation resources. On the resiliency side, plug-in hybrid electric vehicles (PHEV), energy storage systems (ESS), microgrids (MG), and distributed energy resources (DER), can be leveraged to restore critical load in the system when the utility system is not available for extended periods of time. Critical load restoration is a key factor to achieve a resilient distribution system. On the other hand, existing DERs and responsive loads can be coordinated in a market environment to contribute to efficiency of electricity consumption and fair electricity tariffs, incentivizing proactive agents' participation in the distribution system. Resiliency and market applications for distribution systems are highly complex decision-making problems that can be addressed using modern optimization techniques. Complexities of these problems arise from non-linear relations, integer decision variables, scalability, and asynchronous information. On the resiliency side, existing models include optimization approaches that consider system's available information and neglect asynchrony of data arrival. As a consequence, these models can lead to underutilization of critical resources during system restoration. They can also become computationally intractable for large-scale systems. In the market design problem, existing approaches are based on centralized or computational distributed approaches that are not only limited by hardware requirements but also restrictive for active participation of the market agents. In this context, the work of this dissertation results in major contributions regarding new optimization algorithms for market design and resiliency improvement in distribution systems. In the DS market side, two novel contribution are presented: 1) A computational distributed coordination framework based on bilateral transactions where social welfare is maximized, and 2) A fully decentralized transactive framework where power suppliers, in a simultaneous auction environment, strategically bid using a Markowitz portfolio optimization approach. On the resiliency side, this research proposed a system restoration approach, taking into account uncertain devices and associated asynchronous information, by means of a two-module optimization models based on binary programming and three phase unbalanced optimal power flow. Furthermore, a Reinforcement Learning (RL) method along with a Monte Carlo tree search algorithm has been proposed to solve the scalability problem for resiliency enhancement. / Doctor of Philosophy / Distribution systems (DS) are evolving from traditional centralized and fossil fuel generation resources to networks with large scale deployment of responsive loads and distributed energy resources. Optimization-based decision-making methods to improve resiliency and coordinate DS participants are required. Prohibitive costs due to extended power outages require efficient mechanisms to avoid interruption of service to critical load during catastrophic power outages. Coordination mechanisms for various generation resources and proactive loads are in great need. Existing optimization-based approaches either neglect the asynchronous nature of the information arrival or are computationally intractable for large scale system. The work of this dissertation results in major contributions regarding new optimization methods for market design, coordination of DS participants, and improvement of DS resiliency. Four contributions toward the application of optimization approaches for DS are made: 1) A distributed optimization algorithm based on decomposition and best approximation techniques to maximize social welfare in a market environment, 2) A simultaneous auction mechanism and portfolio optimization method in a fully decentralized market framework, 3) Binary programming and nonlinear unbalanced power flow, considering asynchronous information, to enhance resiliency in a DS, and 4) A reinforcement learning method together with an efficient search algorithm to support large scale resiliency improvement models incorporating asynchronous information.