Drawing lines between two plots in Matplotlib

You could use fig.line. It adds any line to your figure. Figure lines are higher level than axis lines, so you don't need any axis to draw it.

This example marks the same point on the two axes. It's necessary to be careful with the coordinate system, but the transform does all the hard work for you.

import matplotlib.pyplot as plt
import matplotlib
import numpy as np

fig = plt.figure(figsize=(10,5))
ax1 = fig.add_subplot(121)
ax2 = fig.add_subplot(122)

x,y = np.random.rand(100),np.random.rand(100)

ax1.plot(x,y,'ko')
ax2.plot(x,y,'ko')

i = 10

transFigure = fig.transFigure.inverted()

coord1 = transFigure.transform(ax1.transData.transform([x[i],y[i]]))
coord2 = transFigure.transform(ax2.transData.transform([x[i],y[i]]))


line = matplotlib.lines.Line2D((coord1[0],coord2[0]),(coord1[1],coord2[1]),
                               transform=fig.transFigure)
fig.lines = line,

ax1.plot(x[i],y[i],'ro',markersize=20)
ax2.plot(x[i],y[i],'ro',markersize=20)


plt.show()

The solution from the other answers are suboptimal in many cases (as they would only work if no changes are made to the plot after calculating the points).

A better solution would use the specially designed ConnectionPatch:

import matplotlib.pyplot as plt
from matplotlib.patches import ConnectionPatch
import numpy as np

fig = plt.figure(figsize=(10,5))
ax1 = fig.add_subplot(121)
ax2 = fig.add_subplot(122)

x,y = np.random.rand(100),np.random.rand(100)

ax1.plot(x,y,'ko')
ax2.plot(x,y,'ko')

i = 10
xy = (x[i],y[i])
con = ConnectionPatch(xyA=xy, xyB=xy, coordsA="data", coordsB="data",
                      axesA=ax2, axesB=ax1, color="red")
ax2.add_artist(con)

ax1.plot(x[i],y[i],'ro',markersize=10)
ax2.plot(x[i],y[i],'ro',markersize=10)


plt.show()