The present knowledge of Lamb shift, fine-, and hyperfine structure of the 2S and 2P states in muonic helium-3 ions is reviewed in anticipation of the results of a first measurement of several 2S → 2P transition frequencies in the muonic helium-3 ion, µ 3 He + . This ion is the bound state of a single negative muon µ − and a bare helium-3 nucleus (helion), 3 He ++ . A term-by-term comparison of all available sources, including new, updated, and so far unpublished calculations, reveals reliable values and uncertainties of the QED and nuclear structure-dependent contributions to the Lamb shift and the hyperfine splitting. These values are essential for the determination of the helion rms charge radius and the nuclear structure effects to the hyperfine splitting in µ 3 He + . With this review we continue our series of theory summaries in light muonic atoms [see Antognini et al., Ann. Phys. 331, 127 (2013); Krauth et al., Ann. Phys. 366, 168 (2016); and Diepold et al., arXiv:1606.05231 (2016)].Key words. muonic atoms and ions -Lamb shift -hyperfine structure -fine structure -QED -proton radius puzzle a authors contributed equally b and electron scattering. This discrepancy has been coined "proton radius puzzle" [7,8,9]. However, the discrepancy exists for the deuteron, too. Interestingly, for the proton and the deuteron, the muonic isotope shift is compatible with the electronic one from the 1S-2S transition in H and D [10,11]. The respective radii are r p (µp) = 0.84087 ( 26) exp (29) th = 0.84087( 39) fm [1, 2] (1) r p (CODATA 14) = 0.87510(610) fm [6] (2) r d (µd) = 2.12562( 13) exp (77) th = 2.12562( 78) fm [4] (3) r d (CODATA 14) = 2.14130(250) fm. [6] (4)Very recently, the CREMA collaboration has measured a total of five transitions in muonic helium-3 and -4 ions [12], which have been analyzed now.