The significance of agile methodologies in project management lies in their ability to promote flexibility, collaboration, and iterative progress. Agile emphasizes adaptive planning, frequent reassessment, and delivery of small, incremental improvements, allowing teams to respond quickly to changing requirements and stakeholder feedback. This approach fosters communication and self-organization among team members, enhancing overall productivity and innovation. Agile methodologies help mitigate risks and improve project outcomes by ensuring that products are better aligned with customer needs and market demands, leading to greater satisfaction and success.