Abstract. A construction of instantons in the context of noncommutative geometry, in particular SU(2) instantons on a noncommutative 4 sphere, has been recently reported. Firstly, a noncommutative principal fibration A(S 4 and a connection ∇ = p • d on it which has a self-dual curvature and charge 1, in some appropriate sense; this is the basic instanton. In [12] infinitesimal instantons -'the tangent space to the moduli space' -were constructed using infinitesimal conformal transformations, that is elements in a quantized enveloping algebra U θ (so(5, 1)). In [10] we looked at a global construction and obtain generic charge 1 instantons by 'quantizing' the action of the Lie groups SL(2, H) and SO(2) on the basic instanton which enter the classical construction [1]. We review all this here.