So, I’ve been studying the Song of Songs and thought I’d share what I’ve been learning. I’ve been reading various articles about the Song of Songs and the various ways that it’s been interpreted over the years. C. Lloyd Carr’s article in Leland Ryken and Tremper Longman III’s “A Complete Literary Guide to the Bible” has been helpful in examining the different interpretations and making the case for why they were inadequate in capturing the meaning of the text and making the case for his own interpretation. All quotes in the following are taken from his article.
The Song of Songs has been interpreted many ways over the centuries. One of the earliest forms of interpretation has been to allegorize the text. Rabbis and Christians have allegorized the song as pertaining to God’s love for his people. The Jews see it as God’s love for Israel and the Christians as Christ’s love for his church (in line with 5:22-33). This leads to pretty wacky interpretations:

ESV Song of Solomon 1:13 My beloved is to me a sachet of myrrh that lies between my breasts.

Rabbinic interpretation saw the woman’s breast as the “two cherubim that formed part of the ‘mercy seat’…and the sachet of myrrh to refer to the Shekinah, the pillar of cloud symbolizing God’s presence that stood between the cherubim in the Holy of Holies in the tabernacle.”
The Christians interpreted the same passage as referring to the “Scriptures of the Old and New Testaments with Christ standing between them.”
Others like Origen saw it as “a marriage song written by Solomon in the form of a drama” The idea was picked up again in the 19th century by Franz Delitzsch. His commentary established the idea that the “Song is a script for dramatic or musical performance.”
But G. Lloyd Carr believes that since there is no plot, movement nor character development it really can’t be considered a play. “The events and interchanges of those eight chapters do not move in a linear direction to a climax and resolution. Instead, is what some writers call ‘ring construction,’ they pivot around the central verses (4:16-5:1), with the last half of the book mirroring the ideas and even the specific vocabulary of the first half.”
Another problem with the drama theory is determining how many characters are speaking. Solomon and the Shulammite bride (6:13) are considered the main characters but some see a third character, the shepherd lover of the Shulammite woman. In this interpretation the Shulammite woman isn’t interested in Solomon’s advances because she’s in love with a shepherd and she resists Solomon attempts to seduce her. Some also see minor characters, “a chorus of women from the city, a male chorus (the woman’s brother) and a mixed chorus of wedding guests.” But it is really hard to determine who is actually speaking and quickly becomes speculative determining who is speaking. Which leads to another problem with the drama theory, the is no true dialogue. “The speakers, even when they are addressing each other, do not carry on conversations. The speech units are essentially monologues.”
Carr’s approach to the song is to treat it as a love poem similar to those of the ancient Near East. He sees a similarity in the use of detailed descriptions:

“All of these collections share another common element: elaborate and often very specifically detailed descriptions of the physical attractions of the parties. This form is often identified as the wasf, a term that in it’s narrow technical meaning is limited to poems composed and sung in honor of the bride or groom as part of the wedding celebration, but it frequently used much more broadly to include any poem describing the adornment and physical charms of a woman.”

Some who see it as a love poem see it as a collection of poems, not a unified poem but Carr sees unity in the poem, he thinks that it has a chiastic structure:

I. Anticipation (1:2-2:7)
II. Found and Lost — and Found (2:8-3:5)
III. Consummation (3:-5:1)
IV. Lost–and Found (5:2-8:4)
V. Affirmation (8:5-14)

Check out the article for a more detailed outline.
For a more outside the box interpretation there is Jim Hamilton’s interpretation of the song as a non-allegorical messianic song:

The Song is about Israel’s shepherd king, a descendent of David, who is treated as an ideal Israelite enjoying an ideal bride in a lush garden where the effects of the fall are reversed. The thesis of this study is that when the Song is heard in the context of the three movement symphony of Torah, Neviim, and Ketuvim, this lyrical theme, the sublime Song, proves to be an exposition of the messianic motif of the Old Testament. I am suggesting that the Song of Songs, read in the context of the Old Testament, is messianic music that we do not need allegorically imaginative ears to hear.
[…]
This messianic understanding of Canticles is not allegorical, nor need it even be
typological, it is strictly historical and canonical. It assumes that the Song of Songs was written from the hope for an anointed king reflected in the rest of the OT,52 but it neither imposes foreign concepts nor imports the NT into the interpretation of the poetry. The garden imagery and the edenic quality of the Song call us to consider the points of contact between the lyrical beauty of the Song, the pristine bliss of Eden, and the one who would bring restoration.

I’ll leave it to you to read the rest to see how he does it but it’s pretty freaky that he sees the bride as being the Messiah’s queen. How does he get around not allegorizing that as the church? (A non-allegorical interpretation that has the Messiah fulfilling the son of David role would have to have a non-allegorical bride fulfilling the Shulammite bride role.)