Recent changes, such as the liberalization of the energy sector and the rapid growth of renewable energy production, have challenged the way the power system is currently operated. In the meantime, the growing share of combined heat and power plants, heat pumps and prosumers interfacing heat and electricity systems provides a source of untapped cross-carrier ﬂexibility that can facilitate the integration of high shares of variable renewable energy sources. In this context, the objective of this thesis is to propose market-based coordination approaches that appropriately interface heat and electricity systems, and aim at an optimal and ﬂexible operation of the overall energy system. By opposition with fully integrated operational models and market clearing procedures, the soft coordination approaches adopted respect these quential order of heat and electricity market clearings. Adopting a top-down approach, the market-based coordination mechanisms developed focus on operational models, bid formats and market clearing procedures that ease market access and coordinate the operation of ﬂexible assets in each energy system and at the interface between the systems. Additionally, adopting a bottom-up approach, the consumer-centric mechanisms developed aim at incentivizing direct participation of decentralized actors and impacting their decisions and interactions towards a social choice. A comprehensive model of the ﬂexible assets in the heat system and at the interface between heat and electricity systems can reveal the full operational ﬂexibility of the overall energy system. Therefore,a special focus is placed on developing mathematical models for the optimal operational of the integrated energy system. In particular, the district heating network holds an untapped energy storage capacity. Modeling complex temporal and spatial dynamics of heat transfer in the pipelines raises computational and optimality challenges, that can be dealt with through convex relaxation approaches. This operational model provides a basis to design novel bid formats and market clearing procedures to harness this operational ﬂexibility in a market environment. In this context, we investigate new market clearing procedures that better account for the interactions between heat and electricity markets. The proposed electricity-aware heat market clearing model is shown to improve the coordination between heat and electricity systems by anticipating the impact of the heat dispatch of combined heat and power plants and heat pumps on the electricity market clearing. Although this approach is shown to be beneﬁcial for both heat and electricity systems, in practice information exchange between the market operators, which is needed to support optimal coordination, might be limited. Therefore, a special focus is placed on revealing hidden information in electricity markets through statistical inference approaches. Despite this improved coordination between heat and electricity market clearings, the operational ﬂexibility of combined heat and powerplants, heat pumps and prosumers in the electricity market is limited by the restricted bid formats allowed. Adequate bid formats should provide a better representation of the techno-economic characteristics of a wide range of ﬂexible assets, including assets at the interface between heat and electricity systems. Acknowledging this limitation, we propose a novel price-region bid format that facilitates the representation of complex infrastructures across multiple areas and time periods. This approach eases market access to assets at the interface between heat and electricity markets, and reveals additional operational ﬂexibility in the power system. Additionally, revealing and harnessing the ﬂexibility of decentralized market participants, such as prosumers, requires a better understanding of their behavior and motivations. Therefore, this thesis focuses on developing consumer-centric mechanisms aiming at coordinating the energy consumption and production of a group of prosumers at the interface between heat and electricity markets. This approach reveals the value of cooperating, in terms of increase in social welfare for the group of prosumers, and proposes allocation mechanisms that fairly redistribute this value among the prosumers. By cooperatively exploiting the synergies between diﬀerent types of loads this approach yields a soft coordination between heat and electricity systems.