The paper investigates random fields in the ball. It studies three typesof such fields: restrictions of scalar random fields in the ball to the sphere, spin, andvector random fields. The review of the existing results and new spectral theory foreach of these classes of random fields are given. Examples of applications to classicaland new models of these three types are presented. In particular, the Mat´ern modelis used for illustrative examples. The derived spectral representations can be utilisedto further study theoretical properties of such fields and to simulate their realisations.The obtained results can also find various applications for modelling and investigatingball data in cosmology, geosciences and embryology.