Various remains have been proposed as those of the princes at various times. The most significant are the bones found in the Tower in 1674 during construction work. The bones were reinterred by Charles II at Westminster Abbey, in an urn in the Henry VII Chapel. In 1933, they were briefly examined by a team of investigators who concluded that they were consistent with the ages of the two princes — but the 1933 examination was conducted without modern forensic methods, and the conclusions have been disputed.
The Church of England has not permitted DNA testing of the Westminster Abbey remains, citing concern about the disturbance of the burial and the lack of certainty that the bones are those of the princes at all. The Richard III DNA findings are relevant to this question because, as Turi King noted in public discussion of the case, the Y-chromosome profile of Richard III could be used as a reference point for comparison against the Westminster bones if testing were permitted. Both princes would have carried the same Y chromosome as their father Edward IV, who was Richard III’s brother. If the male-line haplotype from the skeleton can be established (and the results suggest it can, subject to the complications of the break in the documented male chain), it would be at least a component of a potential future comparison.
Whether such testing will ever be permitted depends on decisions by the Church of England that have not yet been made. The Plantagenet Alliance and other organizations with an interest in the historical question have advocated for testing; the Church and Westminster Abbey have expressed caution. This is a decision for institutions and individuals to make; the science that would enable the testing is already in place.