Do you have an older gas furnace built into the wall or the floor? If yes, then you probably have a millivolt heating system, which isn't compatible. If no, then you're most likely good to use a Nest Learning Thermostat or Nest Thermostat E (Europe). This is based on the fact I can see you have Rh and Rc wires, with a jumper wire from Rh to Rc. You also have a W/E wire but don't have an O/B wire connected, indicating that you do not have a heat pump. As such, your W/E wire is simply your heat wire and it can be connected to W on a Nest thermostat. Only other thing on wires is you don't appear to have a common "C" wire, which in most cases isn't an issue, but mentioning it here for completeness. More details on that here.
