Magnetic resonance elastography (MRE) has evolved significantly since its inception. Advances in motion‐encoding gradient design and readout strategies have led to improved encoding and signal‐to‐noise ratio (SNR) efficiencies, which in turn allow for higher spatial resolution, increased coverage, and/or shorter scan times. The purpose of this review is to summarize MRE wave‐encoding and readout approaches in a unified mathematical framework to allow for a comparative assessment of encoding and SNR efficiency of the various methods available. Besides standard full‐ and fractional‐wave‐encoding approaches, advanced techniques including flow compensation, sample interval modulation and multi‐shot encoding are considered. Signal readout using fast k‐space trajectories, reduced field of view, multi‐slice, and undersampling techniques are summarized and put into perspective. The review is concluded with a foray into displacement and diffusion encoding as alternative and/or complementary techniques.