Update 2: The content and organization of $PlotThemes
in versions 10 and 9 are very different. In Version 10
Charting`$PlotThemes
gives

whereas in Version 9, the content is organized around Charting/Plotting functions (See the picture in original post below.)
The color schemes can be obtained using:
"Color"/. Charting`$PlotThemes
(* BackgroundColor, BlackBackground, BoldColor, ClassicColor, CoolColor,
DarkColor,GrayColor, NeonColor,PastelColor, RoyalColor, VibrantColor, WarmColor,
DefaultColor, EarthColor, GarnetColor, OpalColor, SapphireColor, SteelColor,
SunriseColor, TextbookColor, WaterColor} *)
Grid[{#,Row@(("DefaultPlotStyle"/.(Method/.
Charting`ResolvePlotTheme[#, ListPlot]))/.
Directive[x_,__]:>x)}&/@("Color"/. Charting`$PlotThemes),Dividers->All]

Update: The function that defines the color schemes and styles seems to be ResolvePlotTheme
, which is in the Charting
context in both Version 9 and 10.
?Charting`ResolvePlotTheme
(* too long to copy here ... *)
For example,
Charting`ResolvePlotTheme["Vibrant", ContourPlot]
(* {BaseStyle -> GrayLevel[0.5], BoundaryStyle -> None,
ColorFunction -> (Blend[{Hue[0.5, 1, 0.5], Hue[0.35, 0.5, 0.7],
Hue[0.17, 0.7, 0.9]}, #1] &), ContourStyle -> GrayLevel[1, 0.5],
GridLines -> Automatic,
GridLinesStyle -> Directive[GrayLevel[0.5], Dashing[{0, Small}]],
Method -> {"GridLinesInFront" -> True}} *)
So, one can access the color functions used in these themes using something like;
Grid[{#, ColorFunction /. Charting`ResolvePlotTheme[#, ContourPlot]} & /@
("ContourPlot" /. Charting`$PlotThemes), Dividers -> All]

More generally, one can get the settings for ColorFunction
, ChartStyle
, PlotStyle
BaseStyle
etc. using a similar approach:
Grid[{#, Column@FilterRules[Charting`ResolvePlotTheme[#, PieChart],
{ColorFunction, ChartStyle, BaseStyle}]} & /@
("PieChart" /. Charting`$PlotThemes), Dividers -> All]

PlotTheme
seems to work in Version 9.0.1.0 as an undocumented feature:
?*`*PlotTheme*

After Unprotect
and ClearAttributes[--,ReadProtected]
one can access some details. For example:
?Charting`$PlotThemes

And, despite syntax hightlighting suggesting error, they work as expected:
Row[Plot[Table[BesselJ[n, x], {n, 5}], {x, 0, 10}, Evaluated -> True,
ImageSize -> 400, PlotLabel -> Style[#, 20],
Charting`PlotTheme -> #] & /@ {"Vibrant", "Monochrome"}]

ColorData[97]
with some slight variations between different plots. $\endgroup$Histogram
. $\endgroup$ColorData
indexed colors and information on how to find the gradient used by e.g.BarChart[{Range@99}, PlotTheme -> "Sunrise"]
. Is this more to your liking? Is there something else I can look for to improve my answer? $\endgroup$