Solution 1:

PEP 572 contains many of the details, especially for the first question. I'll try to summarise/quote concisely arguably some of the most important parts of the PEP:

Rationale

Allowing this form of assignment within comprehensions, such as list comprehensions, and lambda functions where traditional assignments are forbidden. This can also facilitate interactive debugging without the need for code refactoring.

Recommended use-case examples

a) Getting conditional values

for example (in Python 3):

command = input("> ")
while command != "quit":
    print("You entered:", command)
    command = input("> ")

can become:

while (command := input("> ")) != "quit":
    print("You entered:", command)

Similarly, from the docs:

In this example, the assignment expression helps avoid calling len() twice:

if (n := len(a)) > 10:
    print(f"List is too long ({n} elements, expected <= 10)")

b) Simplifying list comprehensions

for example:

stuff = [(lambda y: [y,x/y])(f(x)) for x in range(5)]

can become:

stuff = [[y := f(x), x/y] for x in range(5)]

Syntax and semantics

In any context where arbitrary Python expressions can be used, a named expression can appear. This is of the form name := expr where expr is any valid Python expression, and name is an identifier.

The value of such a named expression is the same as the incorporated expression, with the additional side-effect that the target is assigned that value

Differences from regular assignment statements

In addition to being an expression rather than statement, there are several differences mentioned in the PEP: expression assignments go right-to-left, have different priority around commas, and do not support:

  • Multiple targets
x = y = z = 0  # Equivalent: (z := (y := (x := 0)))
  • Assignments not to a single name:
# No equivalent
a[i] = x
self.rest = []
  • Iterable packing/unpacking
# Equivalent needs extra parentheses

loc = x, y  # Use (loc := (x, y))
info = name, phone, *rest  # Use (info := (name, phone, *rest))

# No equivalent

px, py, pz = position
name, phone, email, *other_info = contact
  • Inline type annotations:
# Closest equivalent is "p: Optional[int]" as a separate declaration
p: Optional[int] = None
  • Augmented assignment is not supported:
total += tax  # Equivalent: (total := total + tax)

Solution 2:

A couple of my favorite examples of where assignment expressions can make code more concise and easier to read:

if statement

Before:

match = pattern.match(line)
if match:
    return match.group(1)

After:

if match := pattern.match(line):
    return match.group(1)

Infinite while statement

Before:

while True:
    data = f.read(1024)
    if not data:
        break
    use(data)

After:

while data := f.read(1024):
    use(data)

There are other good examples in the PEP.

Solution 3:

A few more examples and rationales now that 3.8 has been officially released.

Naming the result of an expression is an important part of programming, allowing a descriptive name to be used in place of a longer expression, and permitting reuse. Currently, this feature is available only in statement form, making it unavailable in list comprehensions and other expression contexts.

Source: LicensedProfessional's reddit comment

Handle a matched regex

if (match := pattern.search(data)) is not None:
    # Do something with match

A loop that can't be trivially rewritten using 2-arg iter()

while chunk := file.read(8192):
   process(chunk)

Reuse a value that's expensive to compute

[y := f(x), y**2, y**3]

Share a subexpression between a comprehension filter clause and its output

filtered_data = [y for x in data if (y := f(x)) is not None]