A \emph{sign pattern matrix} is a matrix whose entries are from the set $\{+,-, 0\}$. For   a real matrix $B$, sgn$(B)$ is the sign pattern matrix obtained by replacing each positive (respectively, negative, zero) entry of $B$ by $+$ (respectively, $-$, 0). For a sign pattern matrix $A$, the {\it qualitative class of $A$}, denoted $Q(A)$, is the set of all real matrices whose entries have signs given by the corresponding entries of $A$. An $n\times n$ sign pattern matrix $A$ requires all distinct eigenvalues if every real matrix in $Q(A)$ has $n$ distinct eigenvalues. In the article ``Sign patterns that   require all distinct eigenvalues'', {\it JP J. Algebra Number Theory Appl.}, 2:2 (2002), 161--179, Li and Harris characterized the $2 \times 2$ and $3\times 3 $ irreducible sign pattern matrices that require all distinct eigenvalues, and established some useful general results on $n\times n$ sign patterns that require all distinct eigenvalues. In this talk, we characterize $ 4\times 4 $ irreducible sign   patterns that require four distinct eigenvalues. This is done by characterizing $ 4\times 4 $ irreducible sign patterns that require four distinct real eigenvalues, or require four distinct nonreal real eigenvalues, or require two distinct real eigenvalues and a pair of conjugate nonreal eigenvalues. The last case turns out to be much more involved. The cycle structure of the signed digraph of the sign pattern plays a key role. Some interesting open problems are presented. Three important tools that are used in the paper are the following: the positivity (or negativity) of the discriminant of the characteristic polynomial; the fact that if a square sign pattern matrix $A$ requires all distinct eigenvalues then $A$ requires a fixed number of real eigenvalues; and the known result that if $A$ is an ``$k$-cycle'' sign pattern then it requires $k$ eigenvalues evenly distributed on a circle centered at the origin.