Atmosphere-skimming showers are initiated by cosmic rays with incoming directions such that the full development of the cascade occurs inside the atmosphere without ever reaching the ground. This new class of showers has been observed in balloon-borne experiments such as ANITA, but a characterisation of their properties is lacking. The interplay between the Earth's magnetic field, the long distances over which atmosphere-skimming showers develop, and the low density of the atmosphere they traverse gives rise to several effects that are not seen in downward-going cascades, and require detailed modeling. In this article, we used the latest version of the ZHAireS-RASPASS shower simulation program to tackle this problem, and dwell on the particular phenomena that arises from the peculiar environment in which these showers develop. We focus in particular on the properties of the longitudinal profile of the shower and its fluctuations as a function of cosmic-ray energy, direction and primary mass. We have also studied the phase-space of cosmic-ray arrival directions where detection in high-altitude experiments is more likely, and have found that only in a small range of directions the showers are sufficiently developed before reaching the altitude of the detector. Our results are relevant for the design of high-altitude and in particular balloon-borne experiments, and for the interpretation of the data they collect.