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The spherical Sherrington-Kirkpatrick (SSK) model is one of the simplest spin glass models. It also arises naturally in spherical integrals and statistical applications. SSK is defined by a Hamiltonian associated with a random symmetric matrix. When the temperature is zero, the free energy is equal to the largest eigenvalue of the random matrix. We will discuss how finite temperature cases are also related to random matrix theory. We will also consider the geometry of the Gibbs measure in the presence of an external field.