This paper provides a comprehensive and unbiased review of quantum machine learning, covering both Noisy Intermediate-Scale Quantum (NISQ) technologies and fault-tolerant quantum computing hardware. It delves into fundamental concepts, algorithms, and statistical learning theory relevant to quantum machine learning. The introduction highlights the significance of quantum machine learning in various fields, including quantum chemistry, artificial intelligence, and high-energy physics. It discusses the challenges and potential of quantum machine learning, particularly in the context of NISQ era, where quantum computers are prone to noise and have limited qubit counts. The NISQ era section focuses on Variational Quantum Algorithms (VQAs), which are central to NISQ-era quantum computing. VQAs involve four key components: objective functions, parameterized quantum circuits (PQCs), measurement schemes, and classical optimizers. The paper explores the choice of Hamiltonians, the role of PQCs, measurement techniques, and optimization methods such as stochastic gradient descent. The fault-tolerant quantum computing (FTQC) section discusses algorithms like Quantum Phase Estimation, Quantum Principal Component Analysis, and the Harrow-Hassidim-Lloyd (HHL) algorithm. It also addresses the challenges and potential of FTQC, including the need for quantum error correction and the development of quantum random access memory (QRAM). The statistical learning theory section covers topics such as shadow tomography, classical shadow formalism, and the application of quantum machine learning to quantum data and simulators. The paper concludes with a discussion on the future of quantum machine learning, emphasizing the importance of addressing challenges in the NISQ era and the potential of FTQC for more advanced applications. It also highlights the ongoing debates and controversies surrounding the effectiveness of quantum algorithms and the role of classical machine learning in quantum systems.This paper provides a comprehensive and unbiased review of quantum machine learning, covering both Noisy Intermediate-Scale Quantum (NISQ) technologies and fault-tolerant quantum computing hardware. It delves into fundamental concepts, algorithms, and statistical learning theory relevant to quantum machine learning. The introduction highlights the significance of quantum machine learning in various fields, including quantum chemistry, artificial intelligence, and high-energy physics. It discusses the challenges and potential of quantum machine learning, particularly in the context of NISQ era, where quantum computers are prone to noise and have limited qubit counts. The NISQ era section focuses on Variational Quantum Algorithms (VQAs), which are central to NISQ-era quantum computing. VQAs involve four key components: objective functions, parameterized quantum circuits (PQCs), measurement schemes, and classical optimizers. The paper explores the choice of Hamiltonians, the role of PQCs, measurement techniques, and optimization methods such as stochastic gradient descent. The fault-tolerant quantum computing (FTQC) section discusses algorithms like Quantum Phase Estimation, Quantum Principal Component Analysis, and the Harrow-Hassidim-Lloyd (HHL) algorithm. It also addresses the challenges and potential of FTQC, including the need for quantum error correction and the development of quantum random access memory (QRAM). The statistical learning theory section covers topics such as shadow tomography, classical shadow formalism, and the application of quantum machine learning to quantum data and simulators. The paper concludes with a discussion on the future of quantum machine learning, emphasizing the importance of addressing challenges in the NISQ era and the potential of FTQC for more advanced applications. It also highlights the ongoing debates and controversies surrounding the effectiveness of quantum algorithms and the role of classical machine learning in quantum systems.