When working with functions in TypeScript, understanding how the this keyword is handled is key to avoiding subtle bugs. Arrow functions have a unique way of binding this compared to regular functions. Instead of having their own this, arrow functions capture the this value of the enclosing context at the time they are created. This is often referred to as lexical 'this' binding. In other words, inside an arrow function, this always refers to the value of this from the surrounding code, rather than being set dynamically when the function is called.

You should use arrow functions when you want to preserve the this value from the surrounding context, such as inside class methods that use callbacks or event handlers. However, you should avoid arrow functions as object methods if you expect this to refer to the object itself, since arrow functions do not bind their own this. TypeScript helps you catch these mistakes by providing type checking and error messages when you use this in a way that does not match the expected type. By understanding the lexical binding of this in arrow functions and leveraging TypeScript's type system, you can write safer and more predictable code.