Exploring quantum magnetism has been a long-standing goal in atomic physics, but using conventional ultracold atoms presents several challenges.  The unique properties of ultracold molecules were predicted to circumvent many of these challenges [1]. I will describe recent experiments that have observed many-body quantum magnetism using ultracold molecules in partially filled three-dimensional optical lattices [2], how these experiments have both inspired and validated novel theoretical methods, and implications for future experiments. Because of the many-body, strongly correlated, and entirely beyond mean-field nature of the dynamics, this work is an exemplary case of ``quantum simulation": the use of well-characterized and controllable quantum system to mimic models of interest, whose properties are otherwise difficult or impossible to calculate.

[1] KRA Hazzard, SR Manmana, M Foss-Feig, and AM Rey.  PRL 110, 075301 (2013)

[2] B Yan, SA Moses, B Gadway, JP Covey, KRA Hazzard, AM Rey, DS Jin, and J Ye.  Nature 501, 521 (2013)