The approach of an integrated electricity market is widespread across Europe, since such a market structure has numerous benefits for both the grid and consumers. The current structure and the related policy framework of the electricity markets adopted within the European countries is based on a benchmark model, the so-called Target Model, which describes a reference energy market framework. In this paper, a comprehensive overview of the legislative effort and the resulting Target Model is provided, aiming to set the basis for the description of the adopted electricity markets in Europe. In a second stage, the current status of the Greek electricity market that operates under the Target model scheme is given via the analysis of the involved submarkets, i.e., the forward market, the day-ahead market, the intraday market, and the balancing market. An intricate case study of the Target Model operation in the Greek electricity market within a day of operation is examined, which actually completes the former description. Within the case study, the Greek electricity market is further investigated for its efficiency and the impact on the obtained electricity prices from the first day of the Target Model implementation, which took place in November 2020, and, finally, today is analysed. The results show an overall successful implementation and satisfactory performance of the Target Model in Greece, with an important main result being the reduction of prices in the balancing market and the increase of the intraday market liquidity. However, several challenges are identified and described in detail, while at the same time measures for their confrontation are proposed in order to improve market operation and fully exploit the benefits of the Target Model.