Let $G$ be reductive over the field $F$.

When $F$ is finite, there is Kazdhan-Lustig theory.

When $F$ is archimedean, there is Langlands classification.

When $F$ is supercudpidal and $G$ is $GL(n)$, $SL(n)$, then Bushnell and Kutzko have constructed the unitary dual explicitly.

For general $G$ and non-archimedean $F$, there is no construction of all supercuspidals known.