Hermann Gunkel categorized ten psalms by their subject matter of kingship as the 'royal psalms'. Specifically the royal psalms deal with the spiritual role of kings in the worship of Yahweh. Aside from that single qualification, there is nothing else which specifically links the ten psalms. Each of the psalms make explicit references to their subject, the king. However, it has been posited that other psalms, which do not mention the king directly, may have been written for royalty (e.g. Psalm 22).
Brevard Childs has raised the possibility that the Royal Psalms are strategically scattered throughout the Psalter. According to Childs, these Psalms are often paired with other psalms that give the royal psalms an eschatological and messianic sense.