Electricity price forecasting has become increasingly vital following the liberalization of electricity markets—ushering in a more competitive environment for electricity generation and distribution. Notably, electricity prices in Day-Ahead Markets (DAMs) hold significant sway, influencing decisions made by energy traders. However, modeling electricity prices poses challenges due to their inherent characteristics such as heteroscedasticity, sharp price spikes, and multiple levels of seasonality. Therefore, in this study, we delve into various methodologies from existing literature to forecast electricity spot prices within the Irish DAM. Our focus lies on employing time series and Machine Learning (ML) techniques to predict prices for all 24 hours of each DAM auction facilitated by the Single Electricity Market Operator (SEMO). For this, we begin by providing a concise overview of the electricity market and its functioning, particularly concerning our objective of price forecasting within the DAM. Subsequently, we elucidate the key aspects of the data utilized in this study. Following this, we offer succinct explanations of each model employed, detailing their structures and preparatory steps for the modeling task. Central to our analysis are the results showcasing the performance of each model relative to a benchmark, along with a brief discussion on the significance of predictors in the forecasting process. Finally, based on our findings, we draw conclusions and outline potential avenues for further research and development.