Balladz by Sharon Olds (Jonathan Cape, £12)
“Climbing the stairs, slowly, on my palms / … / how much difference is there, anymore, / between me and a cadaver?” Judging by the now 80-year-old Sharon Olds’s new collection, the answer is: a lot. Across five parts the book covers the death of her partner, spending the first Covid quarantine alone and a tribute to Emily Dickinson in the form of Amherst Balladz. Olds’s familiar subjects of family, sex and the body are here, but also an awareness of her privilege: “For a moment the core of my life / was not desire, but the knowledge of my unearned luck.” Drawing on an unflinching interrogation of the self, these poems pulse with an energy that is thoroughly alive.

Material Properties by Jacob Polley (Picador, £10.99)
The aliveness of the natural world is the main theme of Polley’s first collection since the TS Eliot prize-winning Jackself. The poems have an unforced charm, delighting in the wonder that surrounds us, such as when trying to explain a flower to his son: “Yes, the flower is / saying something somehow / and we must let it.” He also translates some of the Old English riddles found in the 10th-century Exeter Book. His version of De creatura is a gorgeous evocation of the majesty and mundanity of life on Earth: “my scalp spills braids of gold / around my shoulders and down my back, / and I shine where I stand and when I walk / sunlight hangs off my head in chains.”

Was It for This by Hannah Sullivan (Faber, £12.99)
Another Eliot prize winner follows her debut with three more long poems that fruitfully extend the philosophical concerns of 2018’s Three Poems. Happy Birthday is a playful exploration of what it means to turn 41, while the title poem’s blocks of prose poetry focus on the relationships we have with our neighbourhoods. Tenants draws on testimony from the Grenfell inquiry, taking us into the disaster and its aftermath. Sensitively approached, it’s a difficult but necessary read that brings the night back: “The slop of firemen wrestling the carcass down, the heaving dog, / And outside underneath a tree at dawn / The body laid out on the ground. / That rattling sound.”

Brother Poem by Will Harris (Granta, £10.99)
A series of “memory exercises”, many of the poems in Harris’s second collection address a fictional brother. Harris uses this conceit to interrogate what happens when we mourn what hasn’t existed in our lives: “I believed that when we spoke / a token would appear, a third space implied / by our voices, a plane of understanding / entered into, that we knew would stay. / I heard it. And I heard it in you speaking.” As in his Forward prize-winning first collection, Rendang, realities are destabilised through precise, reflexive language, generating an enigmatic beauty that draws you in: “I woke to wake-up in / a cloudless dream, my / tonsils rapt in cotton wool.”

Couplets by Maggie Millner (Faber, £12.99)
A debut verse novel set in Brooklyn, where an unnamed woman in her late 20s leaves her boyfriend to start an affair with another woman. Millner is brilliant at showing how early moments of lust can be existentially unmooring: “Those days, I was something else: / a soft vacuity. A sort of net. / No guilt, no age. No epithet.” The heroic couplets she deploys are pleasing in their wit, especially in the lovers’ text messages to each other: “In one, I praise the wild face she made in sex. / In others, we share travel plans: Trieste.” Reminiscent of Vikram Seth’s The Golden Gate, Couplets is deft, delicate and unexpectedly fun.

• Rishi Dastidar is co-editor of Too Young, Too Loud, Too Different: Poems from Malika’s Poetry Kitchen (Corsair).