Time complexity and space complexity are crucial aspects of algorithm design, as they determine the efficiency and scalability of an algorithm.

Time complexity, measured in Big O notation, represents the amount of time an algorithm takes to complete as a function of the input size. A lower time complexity indicates that an algorithm can handle large inputs efficiently, making it suitable for real-time applications. For example, an algorithm with a time complexity of O(n) is more efficient than one with O(n^2) for large inputs.

Space complexity, also measured in Big O notation, represents the amount of memory an algorithm requires as a function of the input size. A lower space complexity indicates that an algorithm can handle large inputs without consuming excessive memory, making it suitable for systems with limited resources.

Understanding time and space complexity is essential because they directly impact the performance, scalability, and reliability of an algorithm. An algorithm with high time or space complexity may become impractical or even unusable for large inputs, leading to system crashes or slow performance. By optimizing time and space complexity, developers can create efficient algorithms that can handle large datasets and scale well with growing input sizes.