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The emerging Smart Grid paradigm has paved the way for the wide introduction of flexible demand (FD) and energy storage (ES) technologies in power systems, with significant economic, technical, and environmental benefits that will facilitate efficient transition to the low-carbon future. In the deregulated energy sector, the realization of the significant FD and ES flexibility potential should be coupled with their suitable integration in electricity markets. Previous studies have proposed market clearing mechanisms considering FD and ES participation and demonstrated their impact on the system operation. However, these studies have neglected fundamental market complexities, such as modelling and pricing FD non-convexities as well as modelling and analysing the role of FD and ES in imperfect markets. This thesis aims at addressing the above challenges. First of all, a wide literature has demonstrated that uniform marginal pricing cannot generally support competitive equilibrium solutions in markets with non-convexities, yielding surplus sub-optimality effects. Previous work has identified non-convexities associated with the generation side of electricity markets and proposed different approaches to address surplus sub-optimality. This thesis extends this concept to incorporate the demand side. Detailed operational models of different types of FDs capturing their distinct flexibility potentials are proposed. Non-convexities of FD are identified, including options to forgo demand activities as well as discrete and minimum power levels, and resulting surplus sub-optimality effects are demonstrated through simple examples and a larger case study on a test market with day-ahead horizon and hourly resolution. Generalized uplift and convex hull pricing approaches addressing these effects are extended to account for FD non-convexities. Concerning the former, generalized uplift functions for FD participants are proposed, and a new rule is introduced for equitable distribution of the total surplus loss compensation among market participants. Regarding the latter, it is demonstrated that convex hull prices are flattened at periods when FD is scheduled to eliminate surplus sub-optimality associated with the FD ability to redistribute energy requirements across time. Regarding markets with imperfect competition, this thesis provides for the first time theoretical and quantitative evidence of the beneficial impact of FD and ES in limiting market power by the generation side. Quantitative analysis is supported by an equilibrium programming model of the oligopolistic market setting, accounting for the time-coupling characteristics of FD and ES. The decision making process of each strategic electricity producer is modelled through a bi-level optimization problem, which is solved after converting it to a Mathematical Program with Equilibrium Constraints (MPEC) and linearizing the latter through suitable techniques. The oligopolistic market equilibria resulting from the interaction of multiple independent producers are determined by employing an iterative diagonalization method. Case studies on a test market reflecting the general generation and demand characteristics of the GB system quantitatively demonstrate the benefits of FD and ES in limiting generation market power for different scenarios regarding the time-shifting flexibility and location of FD, the size and location of ES, and network congestion, by employing relevant market power metrics from the literature. Furthermore, this thesis explores the market power potential of the FD and ES. Regarding the former, its ability to exercise market power by strategically revealing less time-shifting flexibility to the market is qualitatively analysed through a price-quantity graph in a simplified two-period market. Concerning the latter, although previous studies have demonstrated the ability of large ES units to exercise market power by withholding their capacity, some have adopted modelling approaches exhibiting certain limitations and have not properly analysed the dependency of the extent of exercised market power on ES and system parameters. In this thesis, the decision making process of strategic ES is modelled through a bi-level optimization problem; the upper level determines the optimal extent of capacity withholding at different time periods, maximizing the ES profit, while the lower level represents the market clearing process. This problem is solved after converting it to an MPEC and linearizing the latter through suitable techniques. Case studies on a test market displaying the major generation and demand properties of the GB system quantitatively analyse the extent of capacity withholding and its impact on ES profit and social welfare for different scenarios regarding the size of ES, the characteristics of the generation and demand sides of the market, as well as the location of ES in the presence of network congestion, resorting to relevant market power indexes from the literature.