  We present an account of the ADHM construction of instantons on Euclidean
space-time $\mathbb{R}^4$ from the point of view of noncommutative geometry. We
recall the main ingredients of the classical construction in a coordinate
algebra format, which we then deform using a cocycle twisting procedure to
obtain a method for constructing families of instantons on noncommutative
space-time, parameterised by solutions to an appropriate set of ADHM equations.
We illustrate the noncommutative construction in two special cases: the
Moyal-Groenewold plane $\mathbb{R}^4_\hbar$ and the Connes-Landi plane
$\mathbb{R}^4_\theta$.
