What is the difference between assign() and <<- in R?

The normal approach to writing functions in R (as I understand) is to avoid side-effects and return a value from a function.

contained <- function(x) {
  x_squared <- x^2
  return(x_squared)
}

In this case, the value computed from the input into the function is returned. But the variable x_squared is not available.

But if you need to violate this basic functional programming tenet (and I'm not sure how serious R is about this issue) and return an object from a function, you have two choices.

escape <- function(x){
  x_squared  <<- x^2
  assign("x_times_x", x*x, envir = .GlobalEnv)
}

Both objects x_squared and x_times_x are returned. Is one method preferable to the other and why so?