Neutrality plays an important role as a null model in evolutionary biology. Recent theoretical advances suggest that neutrality is not a unitary concept, and we identify three distinct forms of neutrality. Eu-neutrality means that types do not differ in any measurable way and is thus the idealized form of neutrality. However, individuals or species that do differ in important ways can behave neutrally under some circumstances, both broadening and complicating the applicability of the concept of neutrality. Our second two types of neutrality address two quite different forms of context-dependent neutrality. Circum-neutrality means that two character states have the same direct effect on fitness but do not evolve neutrally because of differences in their circumstances. Iso-neutrality means that two types are equivalent in some population or ecological contexts but not in others, producing an isocline. Confounding of these different definitions has created significant confusion about which models are truly neutral, why some models behave neutrally even when there are large differences in reproductive outputs, and what these different views of neutrality mean to practicing biologists. These complications call into question the acceptance of neutral models as null models and suggest that a better approach is to compare the predictions of models that differ in sources of stochasticity and degree of selection.