The evolution of policy objectives and emergence of new technologies continually challenge the existing wholesale electricity market design. In the framework of standard market design based on locational marginal pricing (LMP) and two-settlement electricity markets, this dissertation investigates two topics for existing and future power systems -- Convergence Bidding (CB) and distribution locational marginal pricing (DLMP). The central theme that connects these two topics is market design -- determining how to create proper incentives to compensate market participants that ensures efficiency and reliability of the power grid. We first empirically test whether the California Independent System Operator's (CAISO) existing two-settlement electricity markets are efficient, and if not, to what extent CB improves market efficiency. We examine the theoretical and empirical tools intended for other financial markets to help us understand the efficacy of CB in the forward and spot electricity markets. In the light of the efficient market hypothesis, Jensen uses the zero-profit competitive equilibrium to describe the condition for market efficiency. This definition of market efficiency directly converts the test of market efficiency into the assessment of return behavior. Following this methodology, we empirically test for market efficiency by evaluating the performance of trading strategies based on market data in the CAISO electric power markets. Our backtest results show that profitable trading opportunities continue to exist in the post-CB period, but the profitability decreases substantially. The decrease in profitability in the post-CB period indicates the improvement of market efficiency, and demonstrates the benefit of CB. The profitability in the post-CB period, however, conveys empirical implications that can be interpreted differently, depending on the level of competition and the level of risk aversion of virtual traders. We further examine the use of DLMP to improve system efficiency in future power systems. DLMP is a modified form of LMP to alleviate congestion induced by electric vehicle (EV) loads on the distribution network. The distribution system operator (DSO) determines distribution locational marginal prices (DLMPs) by solving the social welfare optimization for both the conventional household demand and the EV demand with marginal costs exogenously set to LMPs. We show mathematically that the socially optimal charging schedule can be implemented through a decentralized mechanism where retailers and EV aggregators respond autonomously to the posted DLMPs by maximizing their individual net surplus in the perfectly competitive local DSO market. We further investigate the problem of designing pricing mechanism when LMPs are uncertain. A robust DLMP method is developed for EV charging management under price uncertainty. The efficacy of the proposed use of DLMP is demonstrated by means of case studies using the Bus 4 distribution system of the Roy Billinton Test System (RBTS) and the Danish driving data.