In this mostly expository article, we give streamlined proofs of several well-known Lipschitz extension theorems. We pay special attention to obtaining statements with explicit expressions for the extension constants. One of our main results is an explicit version of a very general Lipschitz extension theorem of Lang and Schlichenmaier. A special case of the theorem reads as follows: If X is any metric space and A⊂X satisfies the condition Nagata(n,c), then any 1
Nearby in the stack
-Lipschitz map
f:A→Y
to a Banach space
Y
admits a Lipschitz extension
F:X→Y
whose Lipschitz constant is at most
1000⋅(c+1)⋅log2(n+2)
. By specifying to doubling metric spaces, this recovers an extension result of Lee and Naor. We also revisit another theorem of Lee and Naor by showing that if
A⊂X
consists of
n
points, then Lipschitz extensions as above exist with a Lipschitz constant of at most