Orthodox Jews are a minority of world Jewry and a growing one, and the two facts together explain most of the movement's current confidence.
Globally, Jews number around fifteen million, roughly split between Israel and the United States with smaller communities in France, Canada, Britain, Argentina, Russia and Australia. In Israel the survey categories are self-descriptive rather than denominational, secular, traditional, religious, Haredi, and the non-Orthodox movements have a much smaller institutional presence than in America, though they have won a series of Israeli court cases on recognition. In the United States, Orthodox Jews are usually found by survey to be under a tenth of Jewish adults.
The demography runs the other way from the raw numbers. Orthodox and especially Haredi families are considerably larger than the Jewish average, and retention among the Orthodox has risen sharply in recent decades, while the non-Orthodox movements have high rates of intermarriage and low rates of transmission. American surveys consistently find the Orthodox share of Jews under eighteen far higher than the share of adults, which is a projection rather than a prediction but a well-founded one.
Two pressures are worth naming. The first is schooling and livelihood: intensive religious education, particularly at the Haredi end, produces communities with high poverty rates and limited secular qualifications, and the resulting arguments about curriculum and state funding are live in New York, London and Israel alike. The second is who is a Jew: because the Israeli rabbinate controls personal status law, Orthodox conversion standards determine who can marry in Israel, which makes an internal religious dispute into a matter of civil rights for hundreds of thousands of people, many of them immigrants from the former Soviet Union.