This issue has been highlighted by the situation of people who want to immigrate to Israel whose laws grant immediate citizenship to any Jew who wants to live there including converts.
But not all Jews will accept all converts as really being Jews. A person is a Jew if and only if their biological mother is Jewish. The status of the father humblingly for men is irrelevant.

It is possible to convert to Judaism although Judaism does not encourage this. And this is where in Israel the issue arises…

The problem is that Orthodox rabbis will not accept conversions to Judaism carried out by non-Orthodox rabbis. (even where as with Conservative rabbis the conversion strictly follows the rules of Jewish law) and are displeased by the more liberal approach to conversion taken by the State of Israel which has been prepared to accept any convert with documentation from any sort of rabbi as a Jew.

One suggestion currently being considered in Israel is the creation of a Conversion Institute which would educate would-be converts in either Orthodox. Conservative or Reform Judaism. The actual conversion would be carried out by the (Orthodox) Chief Rabbinate.

At a conference in early 2000 the Israeli Justice Minister Yossi Beilin suggested the total abandonment of religious criteria for deciding who is and who isn't a member of the Jewish People. However this goes too far for even the Reform movement.

Beilin's proposal points up the growing divide between religious and secular Jews in Israel and fits tidily into the perennial conflict between the secular Zionist definition of the Jews as a nation and the religious definition of the Jews as those people who obey Jewish law.

The plight of the Agunot

These are Orthodox Jewish women whose marriages have ended in divorce but whose husbands will not grant them a religious divorce known as a "get".

Without a "get" these women cannot remarry in an Orthodox synagogue and any children they may have from a later relationship will not be legitimate in Orthodox eyes and will be unable to make a legitimate Jewish marriage themselves.

There is no generally accepted procedure in Jewish law for compelling a husband to grant a "get" and cases have been reported where husbands have demanded to be paid before they will agree to a religious divorce.

The issue of the agunot has provided a major focus for Jews concerned about women's rights. But although their plight is almost universally seen as an injustice. Orthodox respect for the unchangeability of Jewish law has so far prevented a satisfactory solution.