It is a long standing conjecture that F-injectivity deforms. In this talk, we discuss some simple criteria on local cohomology sufficient to give that F-injectivity deforms. These will apply to show that F-injectivity deforms when the non-CM locus of the special fiber is isolated and that F-purity deforms to F-injectivity.. This is joint work with Kazuma Shimomoto and Jun Horiuchi.