Medium- and high-entropy alloys (M/HEAs) mix several principal elements with near-equiatomic composition and represent a model-shift strategy for designing previously unknown materials in metallurgy1,2,3,4,5,6,7,8, catalysis9,10,11,12,13,14 and other fields15,16,17,18. One of the core hypotheses of M/HEAs is lattice distortion5,19,20, which has been investigated by different numerical and experimental techniques21,22,23,24,25,26. However, determining the three-dimensional (3D) lattice distortion in M/HEAs remains a challenge. Moreover, the presumed random elemental mixing in M/HEAs has been questioned by X-ray and neutron studies27, atomistic simulations28,29,30, energy dispersive spectroscopy31,32 and electron diffraction33,34, which suggest the existence of local chemical order in M/HEAs. However, direct experimental observation of the 3D local chemical order has been difficult because energy dispersive spectroscopy integrates the composition of atomic columns along the zone axes7,32,34 and diffuse electron reflections may originate from planar defects instead of local chemical order35. Here we determine the 3D atomic positions of M/HEA nanoparticles using atomic electron tomography36 and quantitatively characterize the local lattice distortion, strain tensor, twin boundaries, dislocation cores and chemical short-range order (CSRO). We find that the high-entropy alloys have larger local lattice distortion and more heterogeneous strain than the medium-entropy alloys and that strain is correlated to CSRO. We also observe CSRO-mediated twinning in the medium-entropy alloys, that is, twinning occurs in energetically unfavoured CSRO regions but not in energetically favoured CSRO ones, which represents, to our knowledge, 将局部化学秩序与任何材料中的结构缺陷相关的第一个实验观察。我们预计，这项工作不仅将扩大我们对这一重要材料类别的基本理解，而且还为通过工程晶格扭曲和当地化学秩序量身定制M/HEA属性提供了基础。