Execution duration: Serverless functions are designed to run for short durations of time, ideally somewhere under 300 seconds only. This is a hard limit set by most cloud providers, however, there are a few workarounds to this as well.

Stateless: Serverless functions are purely stateless, which means that once the function completes its execution or is terminated for some reason, it won't store any data locally on its disk.

Complexity: The smaller you make things, the more complex it's going to become. Although writing functions that perform very particular tasks is a good idea, it can cause complexity issues when you view your application as a whole system. A simple example can break one large application into some ten different functions such that each perform a specific task. Now you need to manage ten different entities rather than just one. Imagine if you had a thousand functions instead.

Lack of tools: Although serverless computing is all at its hype, it still doesn't provide a lot of out-of-the-box tools for management, deployment, and even monitoring. Most of your monitoring tools that you use today were designed for long-running, complex applications; not for simple functions that execute in a mere seconds.

Vendor lock-in: With each cloud provider providing its own unique tool sets and services around serverless computing, you often tend to get tied down to a particular vendor. This means that you cannot change your cloud provider without making some changes to your functions as well.