Functional data analysis is a sub-field of statistics concerned with data generated by stochastic processes 𝑋 (𝑡) ∈ 𝐿2 (𝐼), 𝑡 ∈ 𝐼, where 𝐼 represents an (in-)finite interval. Unlike traditional multivariate observations, functional data are observed at individual time points throughout the interval 𝐼. This unique data structure necessitates novel approaches for analysis. The robustness of these methods is crucial to ensure reliable results, particularly in the presence of anomalies arising from measurement errors or high data variability. This study explores various frameworks designed to address these challenges, demonstrating their efficacy through simulations and real-world data analysis.