Jor-El has been considered to be the most brilliant mind on Krypton. Of his notable achievements, Jor-El was the youngest Kryptonian to be inducted into the Science Council, he was responsible for founding the Phantom Zone and quite possibly has contributed the most to Krypton in his time on the planet. Jor-El also was the first person to know that Krypton was doomed.
Wife to Jor-El. Lara is shown to be a master combatant and of a very keen mind. Jor-El has been mentioned that Lara has been imprisoned inside the Phantom Zone before Jor-El broke her out. Lara has been trained at the Kryptonian Military Academy and has been shown as a very devoted mother and wife to her family.
Kal-El is the last son of Krypton and son of Jor-El and Lara Lor-Van. During Krypton's destruction Kal-El was rocketed from the planet and would later arrive on the planet Earth. Here Kal-El would be adopted by Jonathan and Martha Kent and name Clark. Once he reached adulthood, Clark would use the powers given to him thanks to the yellow sun and become Superman.
Dark Knights of Steel
In Dark Knights of Steel, Jor-El, Lara Lor-Van, and Kal-El all came to Earth when Krypton exploded. Jor-El and Lara ended up becoming Queen and King of a nearby Kingdom and Kal-El was the Prince. Bruce Wayne/Bat-Prince acted as a sort of guard for the family, but secretly he was the son of Jor-El through an affair he had and Bruce was part-Kryptonian. Later revealed Jor El had a another child, Zala El.
In DC's Future State, the members of the El family are: Superman (Jon Kent), Superwoman (Kara Zor-El), Rowan Kent, Ronan Kent, Brandon Kent, Theand'r Ban-El, and Pyrrhos. Khan-El and Alura Van-El are also reportedly members of the family, but it is unclear how they fit in, only that they are married to each other. In the 30th century, Superman (Clark Kent) is known as a legend but makes a couple appearances during the event.