The Phillips Curve is still a useful, albeit imprecise, framework for understanding inflation, in particular its relationship with unemployment.
According to Wikipedia:
The Phillips curve is a single-equation econometric model, named after William Phillips, describing a historical inverse relationship between rates of unemployment and corresponding rates of rises in wages that result within an economy. Stated simply, decreased unemployment, (i.e., increased levels of employment) in an economy will correlate with higher rates of wage rises.
In my understanding, this is also correlated or augmented by inflation expectation. Inflation expectation is like a self-fulfilled prophecy, where public expectation of high inflation leads to more spending, and thus in turn, higher price inflation. In this case, inflation expectation can lead to steeper slope of the Philips curve, and vice versa.
What is noted here is that the Philips curve is becoming flat in the US, where current very low unemployment does not necessarily lead to a higher inflation. Former fed chair Ben Bernanke attributed this to Paul Volcker, who is widely credited with ending the high levels of inflation seen in the United States during the 1970s and early 1980s. As a result, people have high confidence that the Federal Reserve will not let the inflation go wild, as we have seen with the rate hike in 2018 due to risk with inflation due to rate hikes. This confidence leads to a lack of inflation expectation, and thus will not trigger the chain of events that drives up the inflation.