A range of apparatus and methods for providing local and long range data telemetry within a wellbore is described. These apparatus and methods may be combined in a wide variety of ways. In some embodiments data is transmitted across a gap in a drill string using signals of a higher frequency for which an electrical impedance of the gap or of a filter connected across the gap is low. Low-frequency EM telemetry signals may be applied across the gap. The gap and any filter connected across the gap present a high impedance to the low-frequency EM telemetry signals. The described technology may be applied for transferring sensor readings between downhole electrical packages. In some embodiments sensors are electrically connected across electrically insulating gaps in the drill string.