The construction of reduced-order models from a dynamical system can be enhanced when one uses properties of the system, such as the equivariance of the system under the action of a Lie group. Using the equivariance allows the dynamics to be reduced to a subspace where the action of the group has been removed. This effect can be advantageous when applied to systems of transport-dominated phenomena where the transport can be attenuated or even neutralized, and the resulting dynamics may be more efficiently modelled. Here, I discuss constructing reduced-order models using equivariance in systems with transport-dominated phenomena. In addition, i will comment on systems whose equivariance is not explicitly clear and show some approaches used to deal with this when constructing a model.