Noncommutative field theory generalizes field theory to space-time with noncommuting coordinates. This theory arises from limits of M theory and string theory and describes quantum Hall states. It has been studied intensively, revealing new phenomena at both classical and quantum levels. The review covers the basics, active research directions, and applications. Key topics include kinematics, solitons, instantons, gauge theory, quantum field theory, applications to the quantum Hall effect, mathematical aspects, and relations to string and M theory. Noncommutative field theory is defined using an associative algebra with noncommuting coordinates, and its properties are explored through various bases and physical pictures. The theory has connections to condensed matter physics, particularly the quantum Hall effect, and to string theory, where it emerges from limits of M theory and string theory. The review also discusses gauge theories, observables, and the stress-energy tensor, highlighting the challenges in defining local observables and the role of noncommutativity in quantum gravity. The theory has implications for understanding the nature of space-time at short distances and in quantum gravity. The review emphasizes the importance of noncommutative geometry and its connections to mathematical structures, while also addressing the physical relevance and applications of noncommutative field theory.Noncommutative field theory generalizes field theory to space-time with noncommuting coordinates. This theory arises from limits of M theory and string theory and describes quantum Hall states. It has been studied intensively, revealing new phenomena at both classical and quantum levels. The review covers the basics, active research directions, and applications. Key topics include kinematics, solitons, instantons, gauge theory, quantum field theory, applications to the quantum Hall effect, mathematical aspects, and relations to string and M theory. Noncommutative field theory is defined using an associative algebra with noncommuting coordinates, and its properties are explored through various bases and physical pictures. The theory has connections to condensed matter physics, particularly the quantum Hall effect, and to string theory, where it emerges from limits of M theory and string theory. The review also discusses gauge theories, observables, and the stress-energy tensor, highlighting the challenges in defining local observables and the role of noncommutativity in quantum gravity. The theory has implications for understanding the nature of space-time at short distances and in quantum gravity. The review emphasizes the importance of noncommutative geometry and its connections to mathematical structures, while also addressing the physical relevance and applications of noncommutative field theory.