Effort estimation remains a challenging task in the context of Agile-based software development. Some work has focused but lacks an abstract view of effort estimation. Inspired by this, we intend to systematically map literature on Agile software development and its impact on project management, particularly focusing on effort estimation techniques. Following well-established guidelines, the research methodology comprised three phases: (i) planning, (ii) conducting, and (iii) reporting. Covering studies from January 2010 to April 2022, 68 primary studies were analyzed and categorized to address eight research questions. Most papers were published post-2013, with over 48% utilizing evaluation research methods. Model-based approaches constituted over 39% of the selected studies, while 50% were factor-based and over 20% were algorithmic-based. Quality assessment was prevalent, with over 45% of estimation techniques validated. This study provides valuable insights for practitioners and researchers, which offers a foundation for future exploration in the targeted research context.