In this very interesting paper, the authors look at some intricate questions related to subconfigurations of certain generalised quadrangle (GQs). These GQs are of order \((s,t)\) and are constructed as \({\mathbf H(3, q^2)}\), the incidence structure of all the points and lines of a Hermitian surface in \(PG(3, q^2)\). A subquadrangle regular system of order \(m\) on a GQ of order \((s, t)\) is a set \textbf{R} of embedded subquadrangles with the property that every point lies on exactly \(m\) subquadrangles (where \(m\) is a fixed natural number) and if \(m\) is half of the total number of subquadrangles on a point, then \textbf{R} is called a subquadrangle hemisystem. This generalizes the notion of hemisystem that was first looked at by Segre (where lines were considered instead of subquadrangles). The paper under review which has a lot of nice results constructs two infinite families of symplectic subquadrangle hemisystems of \({\mathbf H(3, q^2)}\), where \(q\) is an odd prime admitting \(P{\Omega}^{\pm}_4(q)\) as an automorphism group. The paper also constructs two infinite families of symplectic subquadrangle hemisystems of \(W_3(q^2)\), \(q\) even, admitting the group \(PSL(2, q^2)\) as an automorphism group. The paper also presents some sporadic examples of subquadrangle regular systems of \({\mathbf H(3, q^2)}\).