Plot3D

Plot3D[f,{x,x_min,x_max},{y,y_min,y_max}]

generates a three-dimensional plot of f as a function of x and y.

Plot3D[{f₁,f₂,…},{x,x_min,x_max},{y,y_min,y_max}]

plots several functions.

Plot3D[…,{x,y}∈reg]

takes variables {x,y} to be in the geometric region reg.

Details and Options

Holes are left at any positions where the f_i evaluate to None or anything other than real numbers.
Plot3D treats the variables x and y as local, effectively using Block.
Plot3D has attribute HoldAll and evaluates f only after assigning specific numerical values to x and y.
In some cases it may be more efficient to use Evaluate to evaluate f symbolically before specific numerical values are assigned to x and y.
Plot3D has the same options as Graphics3D, with the following additions and changes:

Axes	True	whether to draw axes
BoundaryStyle	Automatic	how to draw boundary lines for surfaces
BoxRatios	{1,1,0.4}	bounding 3D box ratios
ClippingStyle	Automatic	how to draw clipped parts of surfaces
ColorFunction	Automatic	how to determine the color of surfaces
ColorFunctionScaling	True	whether to scale arguments to ColorFunction
EvaluationMonitor	None	expression to evaluate at every function evaluation
Exclusions	Automatic	x, y curves to exclude
ExclusionsStyle	None	what to draw at excluded curves
Filling	None	filling under each surface
FillingStyle	Opacity[0.5]	style to use for filling
MaxRecursion	Automatic	the maximum number of recursive subdivisions allowed
Mesh	Automatic	how many mesh lines in each direction to draw
MeshFunctions	{#1&,#2&}	how to determine the placement of mesh lines
MeshShading	None	how to shade regions between mesh lines
MeshStyle	Automatic	the style for mesh lines
Method	Automatic	the method to use for refining surfaces
NormalsFunction	Automatic	how to determine effective surface normals
PerformanceGoal	$PerformanceGoal	aspects of performance to try to optimize
PlotLegends	None	legends for surfaces
PlotPoints	Automatic	the initial number of sample points in each direction
PlotRange	{Full,Full,Automatic}	the range of z or other values to include
PlotStyle	Automatic	graphics directives for the style for each surface
PlotTheme	$PlotTheme	overall theme for the plot
RegionFunction	(True&)	how to determine whether a point should be included
ScalingFunctions	None	how to scale individual coordinates
TextureCoordinateFunction	Automatic	how to determine texture coordinates
TextureCoordinateScaling	True	whether to scale arguments to TextureCoordinateFunction
WorkingPrecision	MachinePrecision	the precision used in internal computations

Interactive labeling can be specified for surfaces using Tooltip, StatusArea, or Annotation.
Plot3D[Tooltip[{f₁,f₂,…}],…] specifies that the f_i should be displayed as tooltip labels for the corresponding surfaces.
Tooltip[f,label] specifies an explicit tooltip label for a surface.
PlotStyle->None draws no surface, so effectively does not eliminate hidden surfaces.
Plot3D initially evaluates each function at a grid of equally spaced sample points specified by PlotPoints. Then it uses an adaptive algorithm to choose additional sample points, subdividing at most MaxRecursion times.
You should realize that with the finite number of sample points used, it is possible for Plot3D to miss features in your functions. To check your results, you should try increasing the settings for PlotPoints and MaxRecursion.
With the setting Mesh->All, Plot3D draws mesh lines to show all subdivisions it makes.
The default setting MeshFunctions->{#1&,#2&} draws an x, y mesh on each surface.
The arguments supplied to functions in MeshFunctions and RegionFunction are x, y, z. Functions in ColorFunction and TextureCoordinateFunction are by default supplied with scaled versions of these arguments.
ColorFunction, MeshFunctions, RegionFunction, and TextureCoordinateFunction are all evaluated over each surface.
With the default settings Exclusions->Automatic and ExclusionsStyle->None, Plot3D breaks surfaces at discontinuity curves it detects. Exclusions->None joins across discontinuities.
Possible settings for ScalingFunctions include:
s_z scale the z axis

{s_x,s_y} scale x and y axes

{s_x,s_y,s_z} scale x, y and z axes
Each scaling function s_i is either a string "scale" or {g,g^-1}, where g^-1 is the inverse of g.
Plot3D returns Graphics3D[GraphicsComplex[data]].
Themes that affect 3D surfaces include:

		"DarkMesh"	dark mesh lines
		"GrayMesh"	gray mesh lines
		"LightMesh"	light mesh lines
		"ZMesh"	vertical mesh lines
		"ThickSurface"	add thickness to surfaces
		"FilledSurface"	add filling below surfaces