Evolution by natural selection
Agent: No agent. Described by Charles Darwin and Alfred Russel Wallace, 1858–1859
Source / date: Continuously, in the peer-reviewed biological literature
Reference: Modern synthesis
The baseline, not a rival. Every other entry here is a proposal to supplement or replace this — and it accounts for the appearance of design without a designer, which is precisely why the alternatives have to work so hard.
Class: An undirected process confirmed by evidence. No designer required, and none found.
Why this goes first
Darwin and Wallace presented jointly to the Linnean Society in 1858; On the Origin of Species followed in 1859. The mechanism is unglamorous — heritable variation, differential survival, deep time — and it produces structures that look engineered because the filter does the work a designer would otherwise do.
The Modern Synthesis of the 1930s and 40s joined it to Mendelian genetics, and molecular sequencing confirmed it again from a direction Darwin could not have anticipated: the nested pattern of shared errors in DNA. Broken genes, pseudogenes and inserted viral fragments appear in the same positions in related species. Shared function can be explained by a common designer. Shared mistakes are harder.
What it does not claim — stated plainly
Natural selection explains how existing life diversified. It does not explain how life began. Abiogenesis is a separate and genuinely unsolved problem, and offering the difficulty of the first cell as though it were a difficulty for evolution is a change of subject.
That distinction matters here, because the strongest design arguments cluster at exactly that gap — the origin of the code rather than the diversification of the creatures. Crick and Orgel aimed there deliberately, and they were not cranks about it.