Nonstabilizerness, also colloquially known as magic, quantifies the number of non-Clifford
operations needed in order to prepare a quantum state. In this talk, I will focus long-range nonstabilizerness, which can be defined as the amount of nonstabilizerness that cannot be realized in finite-time by local dynamics (or equivalently by local quantum circuits). I will discuss in particular long-range nonstabilizerness in the context of many-body quantum physics, a task with possible implications for quantum-state preparation protocols and implementation of quantum-error correcting codes. After presenting a simple argument showing that long-range nonstabilizerness is a generic property of many-body states and dynamics, I will restrict to the class of ground states of gapped local Hamiltonians. Focusing on one-dimensional systems, I will present rigorous results in the context of translation-invariant matrix product states (MPSs). By analyzing the fixed points of the MPS renormalization-group flow, I will provide a sufficient condition for long-range nonstabilizerness, which depends entirely on the local MPS tensors. Physically, the condition captures the fact that the mutual information between distant regions of stabilizer fixed points is quantized, and this fact is not changed after applying shallow quantum circuits. I will also discuss possible ramifications in the classification of phases of matter and quantum error correction.