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Background: The role of angular momentum in fission has long been discussed but the observable effects are difficult to quantify. Purpose: We discuss a variety of effects associated with angular momentum in fission and present quantitative illustrations. Methods: We employ the fission simulation model $\mathtt{FREYA}$ which is well suited for this purpose because it obeys all conservation laws, including linear and angular momentum conservation at each step of the process. We first discuss the implementation of angular momentum in $\mathtt{FREYA}$ and then assess particular observables, including various correlated observables. We also study potential effects of neutron-induced fission of the low-lying isomeric state of $^{235}$U relative to the ground state. Results: The fluctuations inherent in the fission process ensure that the spin of the initial compound nucleus has only a small influence on the fragment spins which are therefore nearly uncorrelated. There is a marked correlation between the spin magnitude of the fission fragments and the photon multiplicity. We also consider the dynamical anisotropy caused by the rotation of an evaporating fragment and study especially the distribution of the projected neutron-neutron opening angles, showing that while it is dominated by the effect of the evaporation recoils, it is possible to extract the signal of the dynamical anisotropy by means of a Fourier decomposition. Finally, we note that the use of an isomeric target, $^{235 {\rm m}}$U($n_{\rm th}$,f), may enhance the symmetric yields and can thus result in higher neutron multiplicities for low total fragment kinetic energy.