Some of the foregoing grounds of inadmissibility can be overcome, and some cannot be. If you have a contagious disease, for example, medical treatment might bring a cure. If you are a terrorist, on the other hand, you will never be allowed to enter the United States.
Other people who are permanently inadmissible to the US include (but are not limited to) drug addicts, drug traffickers, people who have committed severe and repeated violations of immigration law.
The situation is complex, however, because certain classes of people are not restricted by the same grounds for inadmissibility that other classes of people are restricted by. They may even be issued immigrant visas and become permanent residents or US citizens, while other classes of people with the same grounds of inadmissibility may not be allowed to enter the US under any visa category.
Between the two extremes of temporary inadmissibility on one hand, and unconditional permanent inadmissibility on the other lies a class of grounds for inadmissibility that may be waived under certain circumstances. This will allow you to enter the United States if you apply for and receive a waiver. In such a case, you might eventually qualify as a US citizen or lawful permanent resident.
Filing Form I-601, Application for Waiver of Grounds of Inadmissibility could allow you to do exactly that, as long as you otherwise qualify for the immigration benefit you are seeking.
It is possible to waive some (but not all) grounds of inadmissibility if you can prove that your inadmissibility would cause “extreme hardship” to a “qualifying relative.”. The I-601 hardship waiver is thought to be granted for the sake of the qualifying relative, not for the beneficiary’s sake because the qualifying relative must be either a US citizen or a lawful permanent resident.