References in chronological order 
 
Arnaud Beauville. 
Variétés Kähleriennes dont la première classe de Chern est nulle.
J. Differential Geom. 18 (1983), no. 4, 755–782 (1984).
Mathscinet     zbMATH          Journal
 
Daniel Greb; Stefan Kebekus; Thomas Peternell. 
Singular spaces with trivial canonical class.
Minimal models and extremal rays (Kyoto, 2011), 67–113, Adv. Stud. Pure Math., 70, Math. Soc. Japan, [Tokyo], 2016.
Mathscinet     zbMATH          Journal            arXiv
 
Jorge Vitório Pereira; Frédéric Touzet. 
Foliations with vanishing Chern classes.
Bull. Braz. Math. Soc. (N.S.) 44 (2013), no. 4, 731–754.
Mathscinet     zbMATH          Journal            arXiv
 
Stéphane Druel. 
A decomposition theorem for singular spaces with trivial canonical class of dimension at most five.
Invent. Math. 211 (2018), no. 1, 245–296.
Mathscinet     zbMATH          Journal            arXiv
 
Stéphane Druel; Henri Guenancia.
A decomposition theorem for smoothable varieties with trivial canonical class. 
J. Éc. polytech. Math. 5 (2018), 117–147.
Mathscinet     zbMATH          Journal            arXiv

Henri Guenancia.
Semistability of the tangent sheaf of singular varieties.
​Algebr. Geom. 3 (2016), no. 5, 508–542.
Mathscinet     zbMATH         Journal           arXiv

 
Daniel Greb; Henri Guenancia; Stefan Kebekus. 
Klt varieties with trivial canonical class: holonomy, differential forms, and fundamental groups.
Geom. Topol. 23 (2019), no. 4, 2051–2124.
Mathscinet    zbMATH          Journal            arXiv
 
Andreas Höring; Thomas Peternell. 
Algebraic integrability of foliations with numerically trivial canonical bundle. 
​Invent. Math. 216 (2019), no. 2, 395–419.
Mathscinet    zbMATH          Journal            arXiv