Aminoacyl-tRNA synthetases (AARSs) are essential enzymes that specifically aminoacylate one tRNA molecule by the cognate amino acid. They are a family of twenty enzymes, one for each amino acid. By coupling an amino acid to a specific RNA triplet, the anticodon, they are responsible for interpretation of the genetic code. In addition to this translational, canonical role, several aminoacyl-tRNA synthetases also fulfill nontranslational, moonlighting functions. In mammals, nine synthetases, those specific for amino acids Arg, Asp, Gln, Glu, Ile, Leu, Lys, Met and Pro, associate into a multi-aminoacyl-tRNA synthetase complex, an association which is believed to play a key role in the cellular organization of translation, but also in the regulation of the translational and nontranslational functions of these enzymes. Because the balance between their alternative functions rests on the assembly and disassembly of this supramolecular entity, it is essential to get precise insight into the structural organization of this complex. The high-resolution 3D-structure of the native particle, with a molecular weight of about 1.5 MDa, is not yet known. Low-resolution structures of the multi-aminoacyl-tRNA synthetase complex, as determined by cryo-EM or SAXS, have been reported. High-resolution data have been reported for individual enzymes of the complex, or for small subcomplexes. This review aims to present a critical view of our present knowledge of the aminoacyl-tRNA synthetase complex in 3D. These preliminary data shed some light on the mechanisms responsible for the balance between the translational and nontranslational functions of some of its components.