The album received positive reviews upon release. At
Metacritic, which assigns a normalized rating out of 100 to reviews from mainstream critics, it received an average score of 77 out of 100, based on 6 publications, indicating "generally favorable reviews". Similarly,
Loud and Quiet said: "Records like
Sun on the Square don't come around very often. ... Where The Innocence Mission has previously been a poster band for the slow-burning record,
Sun on the Square wills you to cling on and not let go from the very beginning. It hunts out the curious minutiae of being alive, saves them and makes them spectacular. In an already strong back catalogue, this album feels like the
crown jewel." Numerous writers complimented the
arrangements found on the album. Timothy Monger of
AllMusic said: "Since paring down their already-hushed
folk pop sound to a mostly acoustic,
drum-less trio in 1997, the band has lived comfortably within the parameters of their tonal world, painting different textures here and there, but otherwise consistently delivering a familiar version of their pastoral
chamber folk with each release." Despite this, they went on to say: "The arrangements on [
Sun on the Square] are somewhat denser and more intricate than on any of the band's previous outings, relying on rich string arrangements, horns, reverberating piano thrums and even a handful of clamorous drum parts."
London in Stereo called
Sun on the Square a "stunning collection of beautifully vulnerable folk songs, ... thanks to typically subtle picking and increasingly orchestrated and gently cinematic accompaniment. Peris’ effortless storytelling once again plays centre stage, weaving through bucolic scenes, touching on love and loss yet always maintaining a blissful hope that ensures the record has the moments of sun its title suggests. The band's first effort for Bella Union is simply gorgeous; mission accomplished."
RTÉ.ie said that: "There may not be a purer sound in pop right now than The Innocence Mission. [They spin] a web of winsome beauty ... [
Sun on the Square is] fragile, wispy and haunting orchestral folk without sounding
tweely sadcore. Who knows what [Karen] is singing about on these delicate and enthralling songs, but there are moments here where The Innocence Mission sound like they're going to dissolve into the ether at any second. It makes them all the more powerful and beautiful."
Uncut also praised Karen's vocals, saying that her voice was "at the fluttering heart of this album; her phrasing and tonal glides are as distinctive as those of
Victoria Williams or
Iris DeMent." while it featured at number three in
NPR's list of the top albums of June 2018. Similarly, the record topped the list on a
Loud and Quiet feature called "July was a bit of a wasteland for new album releases – except for these 7 that we're rating". ==Track listing==