Make a Scatter Plot in matplotlib with dates on x axis and values on y

import pandas as pd
dates = ['2015-12-20','2015-09-12']  
PM_25 = [80, 55]
dates = [pd.to_datetime(d) for d in dates]

plt.scatter(dates, PM_25, s =100, c = 'red')

s sets the size c sets the color

There are a whole bunch of other args as well: http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.scatter

If a plot with data that contains dates, you can use plot_date

Similar to the plot() command, except the x or y (or both) data is considered to be dates, and the axis is labeled.

First convert list to date time, as @RSHARP showed,

dates = [pd.to_datetime(d) for d in dates]

then you can use plot_date

plt.plot_date(dates, PM_25, c = 'red')