Separation Logic (SL) is a foundational tool in program verification,
designed to simplify reasoning about dynamically allocated memory. A
central challenge in this domain involves testing entailments between SL
formulas. In this talk, I will present recent advancements in addressing
the entailment problem in SL, in the presence of inductively defined
predicate symbols. I will provide an overview of key results on the
decidability and complexity of this problem across various SL fragments.
Subsequently, I will delve into an inductive proof procedure that is
sound, complete, and terminating for a specific fragment of inductive
definitions. To conclude, I will outline ongoing and future research
directions in this area.