We study the boundedness of the convolution operator in the case of Morrey spaces. Moreover, their embedding properties and relationship with the Lebesgue spaces are investigated, and basic functional inequalities for these spaces are described. Also, we consider the local Morrey-type spaces and their relationship with Morrey spaces. Additionally, their interpolation properties are described. In particular, by applying the Marcinkiewicz-type interpolation theorem, we obtain an estimate for the norm of the convolution operator in the Morrey spaces, namely the O’Neil-type inequality.