Non-singular points on hypersurfaces over $\mathbb F_q$

In this survey article we investigate hypersurfaces defined over finite fields. More specifically we determine for which hypersurfaces one can ensure the existence of a non-singular point taking the cardinality of our ambient field large if need be. Additionally for such hypersurfaces we will find a lower bound on the cardinality for which a non-singular point is guaranteed. Bibl. 11 titles.