In the estimation of Jeffrey Scott Love in 2013, they 'have received more scholarly attention than any other passage in the text'.
[1]: 195 The following summary of the frame-story is based on the R-recension of the saga, as edited by Christopher Tolkien;[5] the other medieval redactions are substantively similar.
The riddles survive in the three main medieval recensions of Heiðreks saga, known as R, U, and H. The H-version includes the largest number, albeit by virtue of copies of that now fragmentary manuscript made when it was in a more complete state.
[1]: 193–94 The riddles are all in verse, each one stanza long, and well integrated in their style into the genre of Eddaic poetry.
Jeffrey Scott Love has noted that the first four riddles in all three recensions are practically identical and always appear in the same order.
[2] Hannah Burrows has explored the series of 'wave-riddles', in which the waves of the sea are personified as powerful and dangerous women, and has shown the subtle interplay of this series with non-Christian mythology, which reveals how the waves are, 'like Ægir's daughters, both seductive—a source of food and of adventure—and dangerous and unpredictable, taking lives at will'.
[4]: 213 In post-medieval manuscripts the riddles were often transmitted separately from the rest of the saga, emphasising their independent literary interest,[7]: 409 and were the subject of a seventeenth-century commentary by Björn Jónsson á Skarðsá.
[15] Becoming more widely known in the early modern period through printed editions of Heiðreks saga, the 'Óðinn riddle' entered oral tradition.
A modern Swedish children's variant of it runs "vad har tre ögon, tio ben och en svans?"
Twenty-first-century editions and translations focusing solely on the riddles include those by Burrows[7] and Orchard.