Are they particles at all?
Virtual particles are quantized disturbances in physical fields. They aren’t really particles at all. They are called particles because mathematically, they behave as them. This is typical in quantum mechanics as everything can be modeled via a wavefunction.
Let’s take a photon for an example. Photons are quanta of light, i.e., they are the quantum mechanical description of light. It behaves as a particle and as a wave. All around us, electromagnetic fields are emanated by visible light and heat (infrared light). These electromagnetic fields are disturbed by the motion and presence of other photons.
Imagine a shark swimming in the water. The water is disturbed by the motion of the shark and waves are produced. The waves produced cannot exist on their own unless there are others waves or things disturbing it. A wave cannot come from nothing. If you replace the shark with a mass of water, this is the effect that light has on the electromagnetic field.
The same occurs with electrons in electron fields, except that they do not only perturb the electron field, but also the electromagnetic field. This is because they are charged particles. Virtual particles are not particles at all, but are the very perturbations in the field. These perturbations are responsible for electromagnetic attraction and repulsion. When electrons pass by each other, perturbations in the electromagnetic field generate the repulsive force between them, as they are like charged particles. The same phenomenon is responsible for two opposite charges attracting.
This comes from virtual particles exchange. The word “exchange” carries with it wrong connotations. There is no particle that is being passed from one particle to the other. It is difficult to understand intuitively, but can be through mathematics. In order to ignore the math, just know that electromagnetic particles interact because of field perturbations.
As would be expected, antiparticles produce fields as well. For bosons, particle and antiparticle ripples are the same thing; for fermions like electrons and quarks, they are different. If a photon, a boson, passes through an electron field, it causes ripples that are like electron ripples and like positron (antielectron) ripples. They are even and thus carry no net charge. It can do the same thing in a muon field.