The total capital in cryptocurrency markets is around two trillion dollars in 2022, which is almost the same as Apple’s market capitalisation at the same time. Increasingly, cryptocurrencies have become established in financial markets with an enormous number of transactions and trades happening every day. Similar to other financial systems, price prediction is one of the main challenges in cryptocurrency trading. Therefore, the application of artificial intelligence, as one of the tools of prediction, has emerged as a recently popular subject of investigation in the cryptocurrency domain. Since machine learning models, as opposed to traditional financial models, demonstrate satisfactory performance in quantitative finance, they seem ideal for coping with the price prediction problem in the complex and volatile cryptocurrency market. There have been several studies that have focused on applying machine learning for price and movement prediction and portfolio management in cryptocurrency markets, though these methods and models are in their early stages. This survey paper aims to review the current research trends in applications of supervised and reinforcement learning models in cryptocurrency price prediction. This study also highlights potential research gaps and possible areas for improvement. In addition, it emphasises potential challenges and research directions that will be of interest in the artificial intelligence and machine learning communities focusing on cryptocurrencies.