According to the rabbinical law, the Halakhah, a Jew today is anyone who was born of a Jewish mother or who properly converts to Judaism. The status of the father is completely irrelevant. If someone is born a Jew or duly converted to Judaism, that status remains forever after the Halakhah. If a Reform or Conservative Jew cannot prove a Jewish mother or Orthodox conversion, he is "not Jewish" to Orthodox Jews.
Although the Israeli government uses a definition for identifying a Jew that is similar to that of the Halakhah, it supplements it (with the aim of excluding Jewish Christians): whoever does not profess a religion other than the Jewish religion, and the granting of Jewish nationality (to be separated from Israeli citizenship!) is made dependent on this.
In Reform Judaism, until the implementation of Zionism after 1967, Judaism was understood to mean only one Jewish religious affiliation, whereas in secular Zionist circles it was understood to mean a mere ethnicity or nationality.
Because Jews live all over the world, they have adopted different ethnicities, cultures and traditions. Nevertheless, they all feel somehow connected to Israel, feel threatened by anti-Semitism, and those who have remained strict believers share a spiritual bond with the Torah.