If $Z$ is a set of four general points in projective 3-space then a general projection of $Z$ to a general plane is clearly the complete intersection of two conics. If $|Z| = ab$ and $Z$ lies on a smooth quadric surface $Q$ and is the intersection of $a$ lines in one ruling and $b$ lines in the other ruling then again it is clear that a general projection of $Z$ is a complete intersection, now of type $(a,b)$. Beyond this, examples are very far from being obvious. But they exist, and we say that $Z$ is $(a,b)$-geproci if a GEneral PROjection is the Complete Intersection of a curve of degree $a$ and one of degree $b$. A great deal of work has, at this point, gone into the study of geproci sets but they are far from being completely understood. One can relax this condition. For example, consider sets of six points in projective 3-space in linear general position. A general projection does not lie on a conic, but the locus of points of projection for which the image does lie on a conic (hence has a chance to be a complete intersection of type (2,3)) turns out to be a surface of degree 4 called the Weddle surface. This leads to the more general notion of the $d$-Weddle locus for a finite set. To study such a locus, one approach that has borne fruit is via Macaulay duality. This allows us to translate the problem into one involving the cokernel of a certain multiplication map with a linear form, leading to a strong connection between the $d$-Weddle locus and the non-Lefschetz locus of a certain algebra. We will describe these connections. All the results described here are joint with Luca Chiantini, Łucja Farnik, Giuseppe Favacchio, Brian Harbourne, Tomasz Szemberg and Justyna Spond.