In modern and dynamic electricity market, ensuring reliable, sustainable and efficient electricity distribution are pillars of primary importance for grid operation. The high penetration of renewable energy sources and the formation of competitive prices for utility, play a critical role in the wider economic development. Electricity load and price forecasting has been a key focus of researchers in the last decade due to the substantial economic implications for both producers, aggregators and end consumers. Many forecasting techniques and methods have emerged during this period. This paper conducts a extensive and analytical review of the prevailing load and electricity price forecasting methods in the context of the modern wholesale electricity market. The study is separated into three main sections. First, the first section delves into the workings of the electricity market, providing a detailed analysis of the three markets that have evolved, their functions and the key factors influencing overall market dynamics. The second section offers a comprehensive review of the existing literature focusing on load forecasting, highlighting various methodologies, models and their applications in load demand forecasting. This section emphasizes the advances that have been made in all categories of forecasting models and their practical application in different market scenarios. The third section focuses on electricity price forecasting methods, summarizing important research papers investigating various modeling approaches to price forecasting. By examining both traditional and cutting-edge forecasting methods, this review identifies key trends, challenges, and future directions in the field. Overall, this paper provides an in-depth analysis leading to the understanding of the state-of-the-art models in load and price forecasting, being an important resource for researchers and professionals in the energy industry.