We present a sparse spectral method for nonlinear integro-differential
Volterra equations based on the Volterra operator's banded sparsity structure
when acting on specific Jacobi polynomial bases. The method is not restricted
to convolution-type kernels of the form $K(x,y)=K(x-y)$ but instead works for
general kernels at competitive speeds and with exponential convergence. We
provide various numerical experiments on problems with or without known
analytic solutions and comparisons with other methods.