What are the limitations of finite automata?

Could you elaborate on the limitations posed by finite automata in the realm of computational theory? Are there specific tasks or patterns that these automata are unable to recognize or process efficiently? Do they struggle with complexity beyond a certain level? Are there any real-world applications where the limitations of finite automata become particularly apparent or problematic? Additionally, how do these limitations compare to those of other computational models, such as Turing machines? Understanding these constraints could provide valuable insights into the capabilities and limitations of finite automata.