Emergent modified gravity is a new approach to gravity that does not rely on a fundamental space-time metric but instead derives it from canonical phase-space structures. This formulation allows for new types of modified gravity theories that are not of higher-curvature form. The key idea is to use a canonical formulation of general covariance, which enables the construction of new theories where the space-time metric is not fundamental but rather emergent. This approach allows for new phenomena such as dynamical signature changes and non-singular black hole solutions. The canonical formulation distinguishes between configuration degrees of freedom and their velocities, which are turned into momenta as independent phase-space variables. This allows for a more flexible approach to gravity, where the space-time metric is not assumed to be fundamental but is instead derived from the phase-space structure. The canonical formulation of gravity can be given with fewer assumptions because it only requires suitable spatial tensors with a phase-space structure. Unlike in a tensorial formulation, where general covariance is built into the formalism by making use of the tensor transformation law in space-time, general covariance in a canonical formulation is a derived concept that must be demonstrated by an analysis of Poisson brackets and gauge flows of the constraints. This property makes it harder to construct covariant theories of gravity in purely canonical form, but it also provides an opening to new theories of modified gravity because a canonical formulation starts with weaker requirements on the fundamental fields. In particular, it is possible to relax the usual identity between the fundamental canonical configuration field and the induced spatial metric of the corresponding space-time geometry. This identity is realized in all higher-curvature formulations of modified gravity, but it is not necessary in a broader setting of modified canonical gravity. In these new theories, the space-time metric, or even its spatial part, is not fundamental but rather emergent. The emergent spatial metric is uniquely determined by the structure function of the Poisson bracket of two Hamiltonian constraints. The canonical realization of general covariance works by reconstructing spacetime transformations from deformations of spatial hypersurfaces in normal and tangential directions. In a canonical formulation of a theory defined by an action principle directly for the space-time metric or tetrad, such as general relativity or some higher-curvature theory, the normal direction, just as the induced spatial metric on a hypersurface, is uniquely determined by the fundamental space-time metric. If one tries to construct consistent gravity theories purely in a canonical setting, the normal direction is defined more abstractly through the rules by which general covariance is implemented canonically, related to the algebraic form of different Poisson brackets of the constraints that define the theory. The resulting theories may be of interest also for purely classical questions, for instance by providing new covariant equations for phenomenological applications that cannot be obtained from traditional versions of modified gravity. The main motivation of emergent modified gravity then consists in the observation that the space-time metric need not be one of the fundamental fields in an action principle while maintaining the symmetry conditionEmergent modified gravity is a new approach to gravity that does not rely on a fundamental space-time metric but instead derives it from canonical phase-space structures. This formulation allows for new types of modified gravity theories that are not of higher-curvature form. The key idea is to use a canonical formulation of general covariance, which enables the construction of new theories where the space-time metric is not fundamental but rather emergent. This approach allows for new phenomena such as dynamical signature changes and non-singular black hole solutions. The canonical formulation distinguishes between configuration degrees of freedom and their velocities, which are turned into momenta as independent phase-space variables. This allows for a more flexible approach to gravity, where the space-time metric is not assumed to be fundamental but is instead derived from the phase-space structure. The canonical formulation of gravity can be given with fewer assumptions because it only requires suitable spatial tensors with a phase-space structure. Unlike in a tensorial formulation, where general covariance is built into the formalism by making use of the tensor transformation law in space-time, general covariance in a canonical formulation is a derived concept that must be demonstrated by an analysis of Poisson brackets and gauge flows of the constraints. This property makes it harder to construct covariant theories of gravity in purely canonical form, but it also provides an opening to new theories of modified gravity because a canonical formulation starts with weaker requirements on the fundamental fields. In particular, it is possible to relax the usual identity between the fundamental canonical configuration field and the induced spatial metric of the corresponding space-time geometry. This identity is realized in all higher-curvature formulations of modified gravity, but it is not necessary in a broader setting of modified canonical gravity. In these new theories, the space-time metric, or even its spatial part, is not fundamental but rather emergent. The emergent spatial metric is uniquely determined by the structure function of the Poisson bracket of two Hamiltonian constraints. The canonical realization of general covariance works by reconstructing spacetime transformations from deformations of spatial hypersurfaces in normal and tangential directions. In a canonical formulation of a theory defined by an action principle directly for the space-time metric or tetrad, such as general relativity or some higher-curvature theory, the normal direction, just as the induced spatial metric on a hypersurface, is uniquely determined by the fundamental space-time metric. If one tries to construct consistent gravity theories purely in a canonical setting, the normal direction is defined more abstractly through the rules by which general covariance is implemented canonically, related to the algebraic form of different Poisson brackets of the constraints that define the theory. The resulting theories may be of interest also for purely classical questions, for instance by providing new covariant equations for phenomenological applications that cannot be obtained from traditional versions of modified gravity. The main motivation of emergent modified gravity then consists in the observation that the space-time metric need not be one of the fundamental fields in an action principle while maintaining the symmetry condition