When two celestial bodies of vastly different masses, say the Earth and the Sun, attract each other there are five Lagragian libration points, in space, were gravitational and orbital forces are in equilibrium.
These points are abbreviated as L1 through to L5.
L1 to L3 are in direct line with the heavenly bodies. Whereas L4 and L5, the most stable, are on a plain of sixty degrees leading and trailing the orbit of the smaller body. Bearing this fact in mind, depending on the purpose of the mission, one of the most appropriate places to position an artificial satellite would be on or close to one of these libration points.
L1 and L2 are being, or will be, utilized by a number of man made probes. The Gaia mission and the Webb Space telescope are some of the projects planned to take advantage of the L2 libration point.
As L1 to L3 are unstable (i.e., it tends to drift) any craft would be require a propulsion system to maintain their position. To get around the problem of how much propellant will be carried, a Lissajous orbit (click on the magnifying glass, in the link, to get a good visual) is utilized to counter this particular requirement.
My guess is that with the price of fuel and the frequency of available service stations, that an alternative method of improving mileage had to be found.