The Supreme Court held that a permanent resident who pled guilty to a crime involving moral turpitude before the Illegal Immigration Reform and Immigrant Responsibility Act (IIRAIRA) of 1996 still benefits from the Supreme Court's 1963 decision in Fleuti, which provides he would not be considered to be "seeking entry" after a innocent, casual, and brief trip abroad. If the resident is not seeking entry, then he is not subject to numerous additional criminal and noncriminal grounds for removal.
IIRAIRA created a new rule that returning residents are considered to be seeking admission upon return from abroad if they have committed an offense that makes them inadmissible. The Supreme Court held that rule is not retroactive because Congress did not explicitly make it retroactive and it creates a new disability (the noncitizen's inability in this case to travel to Greece briefly to visit his ill parents without being subject to removal upon return). It is thus another application of Landgraf v. USI Film Products, 511 U. S. 244, 263 (1994).
Notably, the Supreme Court held that explicit reliance on prior law by the individual is not required to avoid retroactive application. The majority of the Court also rejected the dissent's argument that the noncitizen's own travel after IIRAIRA is what triggered his removal proceedings and he could have avoided those problems by not traveling.
Vartelas is not a big change for those of us in the Ninth Circuit or Fourth Circuit, since they already had found that the new definition of when a permanent resident would be seeking admission was not retroactive for noncitizens who pled guilty before IIRAIRA. Camins v. Gonzales, 500 F. 3d 872 (CA9 2007); Olatunji v. Ashcroft, 387 F. 3d 383 (CA4 2004).