This review paper provides a comprehensive overview of recent advances in deep learning (DL) for magnetic resonance imaging (MRI) reconstruction. It focuses on various DL approaches and architectures designed to improve image quality, accelerate scans, and address data-related challenges. The paper explores end-to-end neural networks, pre-trained and generative models, and self-supervised methods, highlighting their contributions to overcoming traditional MRI limitations. It also discusses the role of DL in optimizing acquisition protocols, enhancing robustness against distribution shifts, and tackling biases. The review outlines current successes, limitations, and future directions for leveraging DL in MRI reconstruction, emphasizing the potential of DL to significantly impact clinical imaging practices. Key topics include the background on MRI reconstruction, image formation and forward models, conventional model-based image recovery, optimization algorithms, and the computational considerations of different DL reconstruction methods. The paper also covers pre-trained plug-and-play (PnP) methods, generative priors such as GANs and diffusion models, untrained neural networks, and self-supervised methods.This review paper provides a comprehensive overview of recent advances in deep learning (DL) for magnetic resonance imaging (MRI) reconstruction. It focuses on various DL approaches and architectures designed to improve image quality, accelerate scans, and address data-related challenges. The paper explores end-to-end neural networks, pre-trained and generative models, and self-supervised methods, highlighting their contributions to overcoming traditional MRI limitations. It also discusses the role of DL in optimizing acquisition protocols, enhancing robustness against distribution shifts, and tackling biases. The review outlines current successes, limitations, and future directions for leveraging DL in MRI reconstruction, emphasizing the potential of DL to significantly impact clinical imaging practices. Key topics include the background on MRI reconstruction, image formation and forward models, conventional model-based image recovery, optimization algorithms, and the computational considerations of different DL reconstruction methods. The paper also covers pre-trained plug-and-play (PnP) methods, generative priors such as GANs and diffusion models, untrained neural networks, and self-supervised methods.