For at least a century it has been known that multiple factors play a role in the development of complex traits, and yet the notion that there are genes “for” such traits, which traces back to Mendel, is still widespread. In this paper, we illustrate how the Mendelian model has tacitly encouraged the idea that we can explain complexity by reducing it to enumerable genes. By this approach many genes associated with simple as well as complex traits have been identified. But the genetic architecture of biological traits, or how they are made, remains largely unknown. In essence, this reflects the tension between reductionism as the current “modus operandi” of science, and the emerging knowledge of the nature of complex traits. Recent interest in systems biology as a unifying approach indicates a reawakened acceptance of the complexity of complex traits, though the temptation is to replace “gene for” thinking by comparably reductionistic “network for” concepts. Both approaches implicitly mix concepts of variants and invariants in genetics. Even the basic question is unclear: what does one need to know to “understand” the genetic basis of complex traits? New operational ideas about how to deal with biological complexity are needed.