In the Strip Packing (SP) problem, we are given a vertical half-strip \([0,W]\times[0,\infty)\) and a set of \( n \) axis-aligned rectangles of width at most \( W \) . The goal is to find a non-overlapping packing of all rectangles into the strip such that the height of the packing is minimized. A well-studied and frequently used practical constraint is to allow only those packings that are guillotine separable, i.e., every rectangle in the packing can be obtained by recursively applying a sequence of edge-to-edge axis-parallel cuts (guillotine cuts) that do not intersect any item of the solution. In this article, we study approximation algorithms for the Guillotine Strip Packing (GSP) problem, i.e., the SP problem where we require additionally that the packing needs to be guillotine separable. This problem generalizes the classical Bin Packing problem and also makespan minimization on identical machines, and thus it is already strongly \(\mathsf{NP}\) -hard. Moreover, due to a reduction from the Partition problem, it is \(\mathsf{NP}\) -hard to obtain a polynomial-time \((3/2-\varepsilon)\) -approximation algorithm for GSP for any \(\varepsilon > 0\) (exactly as SP ). We provide a matching polynomial time \((3/2+\varepsilon)\) -approximation algorithm for GSP. Furthermore, we present a pseudo-polynomial time \((1+\varepsilon)\) -approximation algorithm for GSP. This is surprising as it is \(\mathsf{NP}\) -hard to obtain a \((5/4-\varepsilon)\) -approximation algorithm for (general) SP in pseudo-polynomial time. Thus, our results essentially settle the approximability of GSP for both the polynomial and the pseudo-polynomial settings.