I have two lists, dates and values. I want to plot them using matplotlib. The following creates a scatter plot of my data.

import matplotlib.pyplot as plt

plt.scatter(dates,values)
plt.show()

plt.plot(dates, values) creates a line graph.

But what I really want is a scatterplot where the points are connected by a line.

Similar to in R:

plot(dates, values)
lines(dates, value, type="l")

, which gives me a scatterplot of points overlaid with a line connecting the points.

How do I do this in python?

I think @Evert has the right answer:

plt.scatter(dates,values)
plt.plot(dates, values)
plt.show()

Which is pretty much the same as

plt.plot(dates, values, '-o')
plt.show()

You can replace -o with another suitable format string as described in the documentation.
You can also split the choices of line and marker styles using the linestyle= and marker= keyword arguments.

For red lines an points

plt.plot(dates, values, '.r-') 

or for x markers and blue lines

plt.plot(dates, values, 'xb-')

In addition to what provided in the other answers, the keyword “zorder” allows one to decide the order in which different objects are plotted vertically.
E.g.:

plt.plot(x,y,zorder=1) 
plt.scatter(x,y,zorder=2)

plots the scatter symbols on top of the line, while

plt.plot(x,y,zorder=2)
plt.scatter(x,y,zorder=1)

plots the line over the scatter symbols.

See, e.g., the zorder demo

They keyword argument for this is marker, and you can set the size of the marker with markersize. To generate a line with scatter symbols on top:

plt.plot(x, y, marker=".", markersize = 10)

To plot a filled spot, you can use marker '.' or 'o' (the lower case letter oh). For a list of all markers, see:
https://matplotlib.org/stable/api/markers_api.html