Lambda functions allow the creation of small anonymous functions and can be passed as arguments to other functions. The map() function applies a lambda function to each element of a list and returns a new list. The filter() function filters a list based on the return value of a lambda function. The reduce() function iteratively applies a lambda function to consecutive pairs in a list and returns a single value. User-defined functions in Python can perform tasks like converting between temperature scales, finding max/min/average of lists, generating Fibonacci series, reversing strings, summing digits in numbers, and calculating powers using recursion.