Cumulative sums of the elements of the list:

Cumulative powers:

Start from the first element of the list:

Use the operator form of FoldList on one argument:

Use the operator form of FoldList on two arguments:

Perform two subsequent permutations:

Perform a chain of cross products:

The head need not be List:

Fold to the right:

Compute successive factorials:

Compute products of successive primes:

Cumulative sums:

Build up a continued fraction:

Build up a nested polynomial (Horner form):

Build up a number from digits:

Form alternating sums:

Generate a random walk:

Find the running maximum of a list:

Find successively deeper parts in an expression:

Successively append to a list:

Build up a binary tree:

Build up a left-branching binary tree:

Make function compositions:

Compute a power using a power tree with successive squaring:

FoldList makes a list of length :

Rest gives a result of length :

Folding with an empty list does not apply the function at all:

Fold gives the last element of FoldList:

Functions that ignore their second argument give the same result as in NestList:

Accumulate is equivalent to FoldList with Plus:

FoldList[f,{}] evaluates to an empty list, without a last element:

Therefore Fold[f,{}] stays unevaluated: