Vector Visualization
The Wolfram Language provides state-of-the-art fully automated visualization of vector functions and data—suitable for representing flows, field lines, and other vector fields of any complexity.
Vector Plots
VectorPlot, ListVectorPlot — plot vectors from a vector field
VectorPlot3D, ListVectorPlot3D — plot vectors from a 3D vector field
SliceVectorPlot3D, ListSliceVectorPlot3D — plot vectors on a slice surface
Stream Plots
StreamPlot, ListStreamPlot — make a stream plot from a vector field
StreamPlot3D, ListStreamPlot3D — make a stream plot from a 3D vector field
Combination Plots
VectorDensityPlot, ListVectorDensityPlot — vector plot with density background
StreamDensityPlot, ListStreamDensityPlot — stream plot with density background
Convolution Plots
LineIntegralConvolutionPlot, ListLineIntegralConvolutionPlot — vector fields transforming an image
Displacement Plots
VectorDisplacementPlot, ListVectorDisplacementPlot — vector fields displacing objects
VectorDisplacementPlot3D, ListVectorDisplacementPlot3D — vector fields displacing 3D objects
Geographic Visualization »
GeoVectorPlot ▪ 
GeoStreamPlot ▪ ...
Complex Visualization »
ComplexVectorPlot ▪ 
ComplexStreamPlot ▪ ...
Options
StreamPoints, VectorPoints — number or placement of streamlines, vectors
StreamScale — scale and size of streamlines
VectorScaling, VectorSizes — scale and size of vectors
StreamStyle, VectorStyle — color and style of streamlines, vectors
StreamMarkers, VectorMarkers — general shape of streamlines, vectors
ColorFunction, Mesh, MeshFunctions — coloring, meshing, contouring, etc. for scalars