Although acculturation psychology is extensively studied in the social sciences, research progress has slowed due to overused methodologies and theories and emerging challenges to core conceptual tenets. Here, we seek to stimulate scientific inquiry into acculturation by integrating underutilized cultural evolutionary perspectives. We propose that cultural evolutionary mechanisms, such as (anti)conformity, prestige bias, payoff bias, and vertical transmission are instrumental in understanding when, why, and how minority- and majority-group members acculturate. The direction and potency of these mechanisms are proposed to be modulated by a combination of contextual and individual factors, resulting in acculturation strategies that at the population level form “cultural evolutionary equilibria.” These equilibria in turn have consequences for the long-term, population-level dynamics of cultural evolution. We outline how our integration of perspectives can allow researchers to model the dynamics of large-scale cultural change, increasing our understanding of the complex challenges faced by today’s diverse societies. Public Abstract Acculturation describes the cultural and psychological changes resulting from intercultural contact. Here, we use concepts from “cultural evolution” to better understand the processes of acculturation. Cultural evolution researchers view cultural change as an evolutionary process, allowing them to borrow tools and methods from biology. Cultural evolutionary mechanisms such as conformity (copying the numerical majority), anti-conformity (copying the numerical minority), prestige bias (copying famous individuals), payoff bias (copying successful people), and vertical cultural transmission (copying your parents) can cause people to adopt elements from other cultures and/or conserve their cultural heritage. We explore how these transmission mechanisms might create distinct acculturation strategies, shaping cultural change and diversity over the long-term. This theoretical integration can pave the way for a more sophisticated understanding of the pervasive cultural shifts occurring in many ethnically diverse societies, notably by identifying conditions that empower minority-group members, often marginalized, to significantly influence the majority group and society.