REVERSED GRADUATED NEUTRAL DENSITY FILTERS have varying density throughout the filter. ZERO filters produce two types of reversed filters - Reversed Filters with hard transition from light to dark in the centre of the filter followed by a soft transition from dark to light on the edge of the filter; and BTR (Broken Topography Reversed Graduated Neutral Density Filters) with a medium transition from light to dark in the centre of the filter followed by a soft transition from dark to light at the edge of the filter. Both types come in strengths ranging from ND4 to ND16 however BTR filters come at a single 100 mm size.
Compared to full and graduated filters, reversed filters are specialty filters. These filters are designed for landscape photographers who shoot with wide angle lens (24 mm or wider on a full frame sensor) and I can hardly think of any other scenario, in which these filters could be generally used. In landscape photography, they are used for shooting sunsets and sunrises and they are most useful in situation when horizon is placed in the bottom part of the frame. If you compose with only a bit of the sky at the top of the frame, graduated filter will do as well, however if a lot of sky is included in the composition, it tends to be considerably darker at the top of the frame. Reversed graduated ND filter is designed to help balance this differences out by darkening most significantly the part of the frame just above the horizon, where the light is strongest.
ZERO Filters produce two different types of reversed filters and they are intended for two slightly different situations. The reversed filter with the harder transition in its middle is more suitable for any scene with a relatively flat horizon while the btr (broken topography reversed) filter with a softer transition in its middle is more suitable for scenes with rather jagged horizons.