NTP2 is a large class of first-order theories introduced by Shelah and generalizing both simple and NIP theories. It provides a natural setting for the theory of forking beyond simplicity, and also contains new important algebraic examples: ultraproducts of p-adics, bounded pseudo real closed fields and certain valued difference fields. I will discuss some open questions about the pure theory of NTP2 theories concentrating on burden, Lascar strong types, simple types, resilience and uniform local character of forking over finite sets (ULCFS).