So far I have seen Richard III, the Duke of Buckingham, Margaret Beaufort as possibly responsible. I have seen the theory that Edward V died from illness or that Richard Duke of York escaped. Some of these seem to be more supported than others but I’d love to know the actual position from scholars.
As far as I can tell, the most common and clearly substantiated theory has always been that it was in fact Richard III, who had the most obvious motive and access. Buckingham may have been involved, but it is unlikely- though not impossible- that he acted alone without Richard's permission. Margaret Beaufort only really had access to them long after their initial imprisonment and it would have been rather bizarre for them to have been thought dead for so long without Richard II producing them to prove the accusations wrong; it being so central to the rebellion organised by Margaret, Elizabeth Woodville, Bishop Morton and Henry VII. For Margaret to have killed them before the rebellion at a more realistic time, around the end of public sightings, would have required her followers somehow infiltrating one of the most heavily guarded rooms in the kingdom. Her husband William Stanley was high-placed in Richard's government, but not with control of the tower, so it would have been exceedingly reckless to attempt it without a good explanation why Stanley's men were in the tower. The theories that one survived, particularly Richard, are fuelled by the imposters that appeared during Henry VII's reign; Perkin Warbeck as Richard, and Lambert Simnel as the Duke of Clarence's son (also in the tower probably killed). Neither of these are seen as very likely to have been the real person, except perhaps by Philippa Gregory for Warbeck (glares). While what exactly happened to them, when, why and what was done with their bodies is a mystery, the princes were almost certainly killed young, that is agreed even by people with different theories. One of them or both may have died from an illness, we really don't know, but it is most likely that the explanation with the most attestation is best. A bit of an Occam's Razor situation:
It was probably Richard.
If you're wondering how a man can kill his own nephews shortly after his brother died of pneumonia and then hold their mother prisoner, well, Richard doesn't seem to have gotten on with the Woodville's, who weren't that popular yet ambitious. And he may have actually believed the boys were canonically illegitimate, given his claims to that affect later. So perhaps he saw himself as the saviour of his house and of the purity of the throne.