Summary: Consider the diffusion process defined by the forward equation \(u_t (t,x) = \frac{1}{2} \{ xu (t,x)\}_{xx} - \alpha \{xu (t,x)\}_x\) for \(t\), \(x \geq 0\) and \(-\infty <\alpha <\infty\), with an initial condition \(u(0,x) = \delta (x-x_0)\). This equation was introduced and solved by Feller to model the growth of a population of independently reproducing individuals. We explore important coalescent processes related to Feller’s solution. For any \(\alpha\) and \(x_0 >0\) we calculate the distribution of the random variable \(A_n (s;t)\), defined as the finite number of ancestors at a time \(s\) in the past of a sample of size \(n\) taken from the infinite population of a Feller diffusion at a time \(t\) since its initiation. In a subcritical diffusion we find the distribution of population and sample coalescent trees from time \(t\) back, conditional on non-extinction as \(t \to \infty\). In a supercritical diffusion we construct a coalescent tree which has a single founder and derive the distribution of coalescent times.