What are some current algorithm(s) for finding if two images are copies of each other? Could anyone enlighten me on what are the current best ways to detect if two images are the same (i.e. a copy or edited copy of each other)? What feature detection method do they use (SIFT, DWT, pixel intensity, etc.)?

I've read a lot of algorithms that focus on detecting similar objects and so on, but I am interested in reading on some for detecting whether two images are copies of each other. I've done some googling and most algorithms/papers I've found are pre-2014 or are about detecting similar images, not exact copies.
This is not a simple problem. You need to define these 'simple edits' and check for all of those. 

For example if you want to find out brightness changes, you cannot effectively use template matching, you would have to go with feature matching (contour, keypoint etc.).

For a general solution, you need to extract a 'signature' from an image which for instance can be done with a combination of histogram and feature points (edge, corner, blob, Shi-Tomasi, LoG etc.)