Flow-based sampling is a promising approach to overcome critical slowing down and topological freezing in lattice field theories, which hinder Monte Carlo sampling as the continuum limit is approached. This method uses normalizing flows, a class of generative models that enable efficient transformations between distributions over lattice field configurations. These models can be used for efficient Monte Carlo sampling, estimating the partition function, drawing correlated samples at different parameters, and performing parameter scans. Recent progress has shown that flow-based models can significantly improve sampling efficiency and accuracy in lattice field theories, including scalar field theories, gauge theories, and quantum chromodynamics (QCD). Normalizing flows are based on invertible transformations that can be parameterized using machine learning techniques. They allow for efficient sampling by transforming a simple distribution into a more complex one. In lattice field theories, these flows can be applied to scalar field theories, gauge theories, and QCD, with particular attention to incorporating symmetries and handling fermions. Flow-based models have been shown to reduce topological freezing and improve the precision of observables in lattice gauge theories, such as U(1) gauge theories. Current research highlights new paradigms in flow-based sampling, including applications to partition functions, parameter dependence, correlated samples, and parallel tempering. These methods offer practical gains in lattice field theory calculations, such as parallel sampling, storage-free ensembles, and improved thermodynamic observables. Flow-based sampling also enables efficient parameter scans and reduces computational costs by allowing independent sampling of subvolumes. In the context of lattice QCD, flow-based models have been applied to theories with dynamical fermions, higher dimensions, and more degrees of freedom. These models have shown significant progress in handling complex lattice field theories, including the Schwinger model, Yang-Mills theories, and QCD in small volumes. The development of gauge-equivariant flows has been particularly important for maintaining symmetries in lattice gauge theories. Future directions include further exploration of new flow architectures, improved training methods, and the integration of flows into standard Markov Chain sampling approaches. The potential of flow-based sampling for lattice field theories is vast, with applications ranging from quantum field theory to condensed matter physics. Continued research is needed to optimize these models and address challenges in training and scaling. The integration of normalizing flows into lattice field theory calculations holds great promise for improving the efficiency and accuracy of Monte Carlo simulations in the field.Flow-based sampling is a promising approach to overcome critical slowing down and topological freezing in lattice field theories, which hinder Monte Carlo sampling as the continuum limit is approached. This method uses normalizing flows, a class of generative models that enable efficient transformations between distributions over lattice field configurations. These models can be used for efficient Monte Carlo sampling, estimating the partition function, drawing correlated samples at different parameters, and performing parameter scans. Recent progress has shown that flow-based models can significantly improve sampling efficiency and accuracy in lattice field theories, including scalar field theories, gauge theories, and quantum chromodynamics (QCD). Normalizing flows are based on invertible transformations that can be parameterized using machine learning techniques. They allow for efficient sampling by transforming a simple distribution into a more complex one. In lattice field theories, these flows can be applied to scalar field theories, gauge theories, and QCD, with particular attention to incorporating symmetries and handling fermions. Flow-based models have been shown to reduce topological freezing and improve the precision of observables in lattice gauge theories, such as U(1) gauge theories. Current research highlights new paradigms in flow-based sampling, including applications to partition functions, parameter dependence, correlated samples, and parallel tempering. These methods offer practical gains in lattice field theory calculations, such as parallel sampling, storage-free ensembles, and improved thermodynamic observables. Flow-based sampling also enables efficient parameter scans and reduces computational costs by allowing independent sampling of subvolumes. In the context of lattice QCD, flow-based models have been applied to theories with dynamical fermions, higher dimensions, and more degrees of freedom. These models have shown significant progress in handling complex lattice field theories, including the Schwinger model, Yang-Mills theories, and QCD in small volumes. The development of gauge-equivariant flows has been particularly important for maintaining symmetries in lattice gauge theories. Future directions include further exploration of new flow architectures, improved training methods, and the integration of flows into standard Markov Chain sampling approaches. The potential of flow-based sampling for lattice field theories is vast, with applications ranging from quantum field theory to condensed matter physics. Continued research is needed to optimize these models and address challenges in training and scaling. The integration of normalizing flows into lattice field theory calculations holds great promise for improving the efficiency and accuracy of Monte Carlo simulations in the field.