The classical Abhidharma commentarial tradition, systematized in Vasubandhu's Abhidharmakosa and in the Theravada commentary literature, distributes the twelve links across three lifetimes to explain how rebirth works mechanically: ignorance and formations belong to a past life; consciousness through becoming unfold within the present life, as the being is conceived, grows, experiences the world and forms new craving and clinging; and birth and ageing-and-death belong to a future life set in motion by the present one's clinging and becoming. On this reading dependent origination explains the mechanics of rebirth without a transmigrating self, exactly the problem Buddhism's denial of a permanent soul creates.
An alternative reading, associated with some modern Theravada meditation teachers and with strands of academic Buddhology skeptical of over-literal Abhidharma systematization, treats the twelve links as unfolding within a single moment of experience, repeated constantly: contact gives rise to feeling, feeling to craving, craving to clinging, and clinging to a momentary "becoming" and "birth" of a reactive self-sense, which subsides, ages and dies within that same span, only for the sequence to begin again with the next contact. On this reading the chain describes the arising and passing of suffering moment to moment, observable directly in meditative attention, rather than a doctrine about literal reincarnation spanning multiple births.
The two readings are not simply rival theories competing for a single correct answer; both have serious canonical and commentarial support, and different lineages within contemporary Buddhism continue to teach one, the other, or both together as complementary levels of the same analysis.