The paper provides an overview of the emerging field of quantum machine learning, which explores the potential of quantum computing to enhance classical machine learning algorithms. It discusses various approaches, including running computationally intensive algorithms efficiently on quantum computers and translating stochastic methods into quantum theory. The authors present a systematic review of methods for pattern classification, such as $k$-nearest neighbour methods, support vector machines, $k$-means clustering, neural networks, decision trees, Bayesian theory, and hidden Markov models, and their quantum counterparts. They also delve into the technical details and potential of future quantum learning theories. The paper highlights the challenges and opportunities in quantum machine learning, emphasizing the need for efficient quantum algorithms and the representation of classical data in quantum systems. Despite the growing interest, a comprehensive theory of quantum learning is still in its early stages, with many open questions and areas for further research.The paper provides an overview of the emerging field of quantum machine learning, which explores the potential of quantum computing to enhance classical machine learning algorithms. It discusses various approaches, including running computationally intensive algorithms efficiently on quantum computers and translating stochastic methods into quantum theory. The authors present a systematic review of methods for pattern classification, such as $k$-nearest neighbour methods, support vector machines, $k$-means clustering, neural networks, decision trees, Bayesian theory, and hidden Markov models, and their quantum counterparts. They also delve into the technical details and potential of future quantum learning theories. The paper highlights the challenges and opportunities in quantum machine learning, emphasizing the need for efficient quantum algorithms and the representation of classical data in quantum systems. Despite the growing interest, a comprehensive theory of quantum learning is still in its early stages, with many open questions and areas for further research.