*Abstract: In 1977, F. Forelli presented the following*

*\smallskip*

*{\bf Theorem.} If the function F is defined in the unit ball B in complex Euclidean space of complex dimension n satisfies the conditions:*

*(1) it is smooth at the origin, and*

*(2) it is holomorphic when restricted along any complex linear disc passing through the origin then, F is holomorphic on B.*

*This is perhaps second only to The Hartogs Analyticity Theorem, as far as the complex analyticity criteria are concerned. After a long silence, this theorem has been studied and generalized in several directions. I would like to report some of the recent developments. [cf. Chirka, Proc. Steklov Inst. Math. (2005/2006); Kim-Poletsky-Schmalz, J. Geom. Anal (2009); Joo-Kim-Schmalz, Math. Ann. (2013 & 2016).]*

*Host: Steven Krantz*