We have developed three approaches for 3D angle decomposition using elastic reverse time migration. The first approach uses time- and space-lag common-image point gathers computed from elastic wavefields. This method facilitates computing angle gathers at sparse and possibly irregularly distributed points in the image. The second approach transforms extended time-lag images to the angle domain using slant stacks along 4D surfaces, instead of using slant stacks along 2D straight lines. The third approach transforms space-lag common-image gathers to the angle domain. The three proposed methods solve a system of equations that handles dipping reflectors, and they yield angle gathers that are more accurate compared with those obtained via alternative existing methods. We have developed our methods using 2D and 3D synthetic and field data examples and found that they provide accurate opening and azimuth angles and they can handle steeply dipping reflectors and converted wave modes.