Abstract: In the first part of the presentation, we explain a Feller’s test for explosions of one-dimensional continuous stochastic Volterra processes of convolution type. We focus on dynamics governed by nonsingular kernels, which preserve the semimartingale property of the processes and introduce memory features through a path-dependent drift. The results are illustrated with three specifications of the dynamics: the Volterra square-root diffusion, the Volterra Jacobi process, and the Volterra power-type diffusion. In the second part of the presentation, we provide an Osgood’s test for explosions of one-dimensional stochastic Volterra equations with additive noise, featuring kernels from a family that includes the fractional kernel.