The electric field strength between coplanar electrodes is calculated employing conformal transformations. The electron multiplication factor is then computed in the nonuniform field region. These calculations have been made for different gap lengths, voltages, and also for different gases and gas pressures. The configuration results in a curved discharge path. It is found that the electron multiplication is maximum along a particular flux line and the prebreakdown discharge is expected to follow this flux line. Experimental tubes incorporating several coplanar gaps have been fabricated. Breakdown voltages have been measured for various discharge gaps and also for various gases such as xenon, helium, neon, argon, and neon-argon mixture (99.5:0.5) at different filling pressures. The variation of breakdown voltage with pressure and gap length is discussed. The observed discharge paths are curved and this is in agreement with theoretical results. A few experimental single-digit coplanar gas-discharge displays (CGDD's) with digit height of 5 cm have been fabricated and dependence of their characteristics on various parameters, including spacing between top glass plate and bottom substrate, have been studied.