The ongoing decarbonization of energy systems introduces challenges to the operation of deregulated day-ahead electricity markets, due to the intermittency of renewable energy sources. A main challenge refers to the short-term risk, that market participants are faced with, deriving from the highly uncertain spot prices. Due to this uncertainty, the scheduling of participants becomes cumbersome, especially when their portfolios comprise assets, exhibiting time-coupling and lumpy characteristics. The USA market paradigm inherently addresses this issue, as it prescribes the explicit declaration of participants' operational parameters to the market operator, hence transferring to the latter the responsibility of satisfying participants' operational constraints. However, the European market paradigm, traditionally invited participants to submit strictly economic hourly orders, rendering them responsible for satisfying their operational constraints and ill-equipped to sufficiently express their preferences. In order to allow participants to implicitly convey their operational characteristics to the market, and hedge the price uncertainty risk, European markets have introduced non-convex offering structures, the most prominent of which is block orders (BOs). BOs constitute intertemporal power offers, and are characterized by an all-or-nothing condition, implying that each BO is either accepted or rejected by the market in its entirety. This thesis proposes novel optimal offering models, which enable generation, energy storage, and flexible demand participants, to leverage both eligible offering structures of European markets, i.e., hourly orders and BOs. Moreover, it studies the suitability of different types of BOs towards implicitly encompassing the operational properties of each type of considered participants. Furthermore, it employs the proposed models in large-scale studies considering UK market data, showcasing their relevance and applicability, in that the associated computational cost is not prohibitive towards their employment. Finally, it focuses on both price-taking and strategic participant behaviour, investigating the implications of introducing BOs, on individual participants' welfare and social welfare.