Self-assessment encourages students to critically evaluate their own work, identifying strengths and areas for improvement. It fosters metacognition—thinking about one’s own thinking—and helps learners develop independence and responsibility for their learning journey.

Peer-assessment involves students reviewing and providing feedback on each other's work. This approach enhances analytical skills, encourages collaborative learning, and broadens students' perspectives by exposing them to different approaches and ideas.

Advantages:

Enhanced reflective skills: Students learn to critically assess their own progress and understand their learning process better.
Development of critical thinking: Both self- and peer-assessment require learners to evaluate quality and justify their judgments.
Increased engagement and motivation: Students often find these methods more collaborative and meaningful, fostering a sense of ownership over their learning.
Preparation for real-world skills: These assessments mirror professional environments where feedback and self-evaluation are essential.

Challenges:

• Students might lack the experience to judge work accurately, which can lead to biased feedback.
• Without proper training, peer feedback might be ineffective or unconstructive.
• Implementing these assessments requires additional planning and reflection, which might be perceived as time-consuming.

Self- and peer-assessment create a classroom environment where students feel valued and responsible for their learning. It humanizes education by encouraging open communication, trust, and mutual respect. For example, when students review each other's presentations or essays, they learn to appreciate different styles and viewpoints, fostering empathy and a deeper understanding of the learning process.

Here’s a short video that nicely explains the value of self- and peer-assessment: 

References:

Anders Ericsson, K. (2007). Deliberate Practice and Expertise. Cambridge University Press.
Topping, K. (2009). Peer assessment. Theory into Practice, 48(1), 20-27.
Boud, D., & Associates. (2010). Assessment & Learning in Higher Education. Routledge.