Handling null and undefined values in programming can be challenging, as they often lead to errors and inconsistencies. The Maybe data type, also known as Option, provides a structured approach to manage the absence of values by encapsulating them as either Just a value or Nothing, thus avoiding semantic confusion associated with null and undefined. This concept is implemented in TypeScript using the ts.data.maybe library, allowing developers to define data structures with properties that may or may not hold a value, ensuring that the compiler enforces checks and prevents runtime errors. Similarly, the Either data type offers a way to handle operations that may fail by distinguishing between Right, indicating success, and Left, indicating error, which reduces the complexity of error-handling code. Both container types, Maybe and Either, promote cleaner, more functional code by providing APIs for safely operating on values, thereby enhancing code readability and maintainability.