In practice, the process is as follows: if you are a descendant of a Jew through any line — mother, father, grandfather or grandmother — you have the right to immigrate under the Law of Return.
For great-grandchildren, this right is implemented through the issuance of permanent residency (PR) rather than immediate citizenship.
After three years of residence, and provided that your “center of life” is genuinely in Israel — renting accommodation, formal employment, children enrolled in school, enrollment in a health fund — you are fully entitled to apply for citizenship.
The key criterion is proof of center of life. This requires demonstrating real integration into Israeli society, not just physical presence. Supporting evidence includes rental agreements, utility bills, registration at medical institutions, and school documentation for children.