Recursion is a programming technique where a function calls itself directly or indirectly to solve a problem. It’s a powerful and elegant approach commonly used to solve problems that can be broken down into smaller, similar subproblems.

Here are some key points about recursion:

1. Base Case: Recursion involves breaking down a problem into smaller instances of the same problem. Each recursive function call works on a smaller or simpler version of the original problem. Eventually, the problem becomes small enough that it can be solved directly without further recursion. This stopping condition is called the base case, and it prevents the recursion from continuing indefinitely, leading to a termination of the recursive process.

2. Recursive Step: In addition to the base case, a recursive function includes a recursive step, which is where the function calls itself with modified input parameters. This step progresses towards the base case by reducing the problem’s size or complexity with each recursive call.

3. Memory Usage: Recursion uses the call stack to manage function calls. Each recursive call adds a new frame to the call stack, which stores information such as local variables, return addresses, and parameters. When the base case is reached, the function calls begin to return, and the call stack shrinks accordingly. Recursive algorithms can be memory-intensive, especially if the depth of recursion is significant or if each function call requires a large amount of memory.

4. Termination: It’s crucial to ensure that a recursive function eventually reaches its base case(s) to avoid infinite recursion, which can lead to a stack overflow error and program termination. A well-designed recursive function should make progress towards the base case with each recursive call and handle all possible input cases.

5. Examples: Recursion is commonly used to solve problems that can be divided into smaller subproblems, such as searching, sorting, tree traversal, and mathematical computations like factorial or Fibonacci sequence generation.

Here’s a simple example of a recursive function to calculate the factorial of a non-negative integer:

def factorial(n):
    # Base case: factorial of 0 or 1 is 1
    if n == 0 or n == 1:
        return 1
    # Recursive step: n! = n * (n-1)!
    return n * factorial(n - 1)

# Example usage:
print(factorial(5))  # Output: 120 (5! = 5 * 4 * 3 * 2 * 1)

In this example, the factorial() function calls itself with the argument n - 1 until it reaches the base case (n == 0 or n == 1), at which point the recursion stops and the factorial value is calculated by multiplying the current value of n with the result of the recursive call.