The modern expectations-augmented version says inflation equals expected inflation, minus a coefficient times the unemployment gap, plus supply shocks. Written that way, the curve says slack matters at the margin but inflation-expectations do most of the work.
Its slope flattened dramatically after the 1990s, which is why the relationship looked dead for two decades. The 2021 to 2023 episode suggested it is non-linear: nearly flat when the labour market is loose and steep when vacancies far exceed job seekers.
Example: expected inflation 2.5%, unemployment 3.8% against a nairu of 4.4%, and a slope coefficient of 0.3. Predicted inflation is 2.5 + 0.3 x 0.6 = 2.68%, so slack explains only a fifth of a point of the overshoot.
Related: nairu, inflation-expectations, output-gap, taylor-rule, unemployment-rate