Context: Dynamic software product lines (DSPLs) have considerably increased their adoption for variability management for self-adaptive systems. The most widely used models for managing the variability of DSPLs are the MAPE-K control loop and context-aware feature models (CFMs). Aim: In this paper, we review and synthesize evidence of using variability constraint approaches, methodologies, and challenges for DSPL. Method: We conducted a systematic mapping, including three research questions. This study included 84 papers published from 2010 to 2021. Results: The main results show that open-dynamic variability shows a presence in 57.1% of the selected papers, and on the other hand, closed-dynamic variability appears in 38.1%. The most commonly used methodology for managing a DSPL environment is based on proprietary architectures (60.7%), where the use of CFMs predominates. For open-dynamic variability approaches, the MAPE-K control loop is mainly used. The main challenges in DSPL management are based on techniques (28.6%) and open variation (21.4%). Conclusions: Open-dynamic variability has prevailed over the years as the primary approach to managing variability in DSPL, where its primary methodology is the MAPE-K control loop. Response RQ3 requires further review.