Exoplanets are typically thought to form in protoplanetary disks left over from protostellar disk of their newly formed host star. However, additional planetary formation and evolution routes may exist in old evolved binary systems. Here we discuss the implications of binary stellar evolution on planetary systems in such environments. In these binary systems stellar evolution could lead to the formation of symbiotic stars, where mass is lost from one star and could be transferred to its binary companion, and may form an accretion disk around it. This raises the possibility that such a disk could provide the necessary environment for the formation of a new, second generation of planets in both circumstellar or circumbinary configurations. Pre-existing first generation planets surviving the post-MS evolution of such systems would be dynamically effected by the mass loss in the systems and may also interact with the newly formed disk. Such planets and/or planetesimals may also serve as seeds for the formation of the second generation planets, and/or interact with them, possibly forming atypical planetary systems. Second generation planetary systems should be typically found in white dwarf binary systems, and may show various observational signatures. Most notably, second generation planets could form in environment which are inaccessible, or less favorable, for first generation planets. The orbital phase space available for the second generation planets could be forbidden (in terms of the system stability) to first generation planets in the pre-evolved progenitor binaries. In addition planets could form in metal poor environments such as globular clusters and/or in double compact object binaries. Observations of exo-planets in such forbidden or unfavorable regions could possibly serve to uniquely identify their second generation character. Finally, we point out a few observed candidate second generation planetary systems, including Gl 86, HD 27442 and all of the currently observed circumbinary planet candidates. A second generation origin for these systems could naturally explain their unique configurations.