When you know you'll want the full list of items constructed (for instance, for passing to a function that would modify that list in-place). Or when you want to force the arguments you're passing to zip() to be completely evaluated at that specific point.
zip computes all the list at once, izip computes the elements only when requested.
One important difference is that 'zip' returns an actual list, 'izip' returns an 'izip object', which is not a list and does not support list-specific features (such as indexing):
So, if you need a list (an not a list-like object), just use 'zip'.
Apart from this, 'izip' can be useful for saving memory or cycles.
E.g. the following code may exit after few cycles, so there is no need to compute all items of combined list:
lst_a = ... #list with very large number of items
lst_b = ... #list with very large number of items
#At each cycle, the next couple is provided
for a, b in izip(lst_a, lst_b):
if a == b:
break
print a
using zip would have computed all(a, b) couples before entering the cycle.
Moreover, if lst_a and lst_b are very large (e.g. millions of records), zip(a, b) will build a third list with double space.
The itertools library provides "iterators" for common Python functions. From the itertools docs, "Like zip() except that it returns an iterator instead of a list." The I in izip() means "iterator".
Python iterators are a "lazy loaded" sequence that saves memory over regular in-memory list. So, you would use itertools.izip(a, b) when the two inputs a, b are too big to keep in memory at one time.
Look up the Python concepts related to efficient sequential processing: