Well, a good starting point is Rambam in his Mishneh Torah, Hilchos Teshuva 10:3:
וְכֵיצַד הִיא הָאַהֲבָה הָרְאוּיָה. הוּא שֶׁיֹּאהַב אֶת ה' אַהֲבָה גְּדוֹלָה יְתֵרָה עַזָּה מְאֹד עַד שֶׁתְּהֵא נַפְשׁוֹ קְשׁוּרָה בְּאַהֲבַת ה' וְנִמְצָא שׁוֹגֶה בָּהּ תָּמִיד כְּאִלּוּ חוֹלֶה חֳלִי הָאַהֲבָה שֶׁאֵין דַּעְתּוֹ פְּנוּיָה מֵאַהֲבַת אוֹתָהּ אִשָּׁה וְהוּא שׁוֹגֶה בָּהּ תָּמִיד בֵּין בְּשִׁבְתּוֹ בֵּין בְּקוּמוֹ בֵּין בְּשָׁעָה שֶׁהוּא אוֹכֵל וְשׁוֹתֶה. יֶתֶר מִזֶּה תִּהְיֶה אַהֲבַת ה' בְּלֵב אוֹהֲבָיו שׁוֹגִים בָּהּ תָּמִיד כְּמוֹ שֶׁצִּוָּנוּ בְּכָל לְבָבְךָ וּבְכָל נַפְשְׁךָ. וְהוּא שֶׁשְּׁלֹמֹה אָמַר דֶּרֶךְ מָשָׁל (שיר השירים ב ה) "כִּי חוֹלַת אַהֲבָה אָנִי". וְכָל שִׁיר הַשִּׁירִים מָשָׁל הוּא לְעִנְיָן זֶה
What is the proper [degree] of love? That a person should love God with a very great and exceeding love until his soul is bound up in the love of God. Thus, he will always be obsessed with this love as if he is lovesick.
[A lovesick person's] thoughts are never diverted from the love of that woman. He is always obsessed with her; when he sits down, when he gets up, when he eats and drinks. With an even greater [love], the love for God should be [implanted] in the hearts of those who love Him and are obsessed with Him at all times as we are commanded [Deuteronomy 6:5: "Love God...] with all your heart and with all soul."
This concept was implied by Solomon [Song of Songs 2:5] when he stated, as a metaphor: "I am lovesick." [Indeed,] the totality of the Song of Songs is a parable describing [this love].
So according to Rambam, in the same way that a person who is in love with a woman to such a degree that she is always in his mind, so should the relationship be with G-d, and Rambam explains that Shir HaShirim is the parable that showcases this message.
Note the Metzudos Dovid on the opening pasuk:
יספר בו את כל תוקף קשור אהבה העזה ודבוק האמתי שבין האל יתברך ובין עמו בית ישראל ואחז במשל מן האהבה הנמרצת וחזקה שבין החושק וחשוקתו
It relates in it, all the strength/power (of G-d) is connected with intense and true love that is between G-d, blessed be He, and His people, the House of Israel. And it is presented with a parable of the vigorous and strong love between the desirer and his lover.
(Indeed, parenthetically, it is worth noting that since this is such a prominent theme within the megillah it actually gave rise to a major argument amongst the Tannaim as to whether it was appropriate to be read or whether it is "מְטַמָּא אֶת הַיָּדַיִם" - "defiles the hands" - Refer to Mishnah Yadayim 3:5)
If you specifically want a "modern" perspectives Rabbi Adin Steinsaltz had a commentary available online here. In his introduction (p.10) he writes the following:
The love between man and woman, which is the focus of the entire book, has been understood throughout the generations as an allegory for the relationship between the people of Israel as a whole and the Holy One. The Song of Songs evokes a relationship of intense longing and intimacy using very specific imagery...