How to set xlim and ylim for a subplot

You should use the OO interface to matplotlib, rather than the state machine interface. Almost all of the plt.* function are thin wrappers that basically do gca().*.

plt.subplot returns an axes object. Once you have a reference to the axes object you can plot directly to it, change its limits, etc.

import matplotlib.pyplot as plt

ax1 = plt.subplot(131)
ax1.scatter([1, 2], [3, 4])
ax1.set_xlim([0, 5])
ax1.set_ylim([0, 5])


ax2 = plt.subplot(132)
ax2.scatter([1, 2],[3, 4])
ax2.set_xlim([0, 5])
ax2.set_ylim([0, 5])

and so on for as many axes as you want.

or better, wrap it all up in a loop:

import matplotlib.pyplot as plt

DATA_x = ([1, 2],
          [2, 3],
          [3, 4])

DATA_y = DATA_x[::-1]

XLIMS = [[0, 10]] * 3
YLIMS = [[0, 10]] * 3

for j, (x, y, xlim, ylim) in enumerate(zip(DATA_x, DATA_y, XLIMS, YLIMS)):
    ax = plt.subplot(1, 3, j + 1)
    ax.scatter(x, y)
    ax.set_xlim(xlim)
    ax.set_ylim(ylim)