What are the disadvantages of ECC?

When it comes to Elliptic Curve Cryptography, or ECC, what are some of the potential drawbacks or disadvantages that one should be aware of? Are there any security concerns or limitations in terms of its usage, and how might these affect its adoption or implementation in various applications and systems? It's important to have a comprehensive understanding of both the strengths and weaknesses of ECC in order to make informed decisions about its use.