For decades spacecraft would fly direct to the moon and then brake into lunar orbit, but these days most spacecraft take long circuitous routes, dancing on the edge of stability near the lagrange points of the sun-earth-moon system. These techniques save propellent at the expense of time and navigation complexity.
They use the theory of weak stability boundaries and ballistic capture in the 3 body problem, to make this possible, and it's an idea which was first discovered in the early 1990's and has now become the main route for modern spacecraft.

Some of the orbit visualizations use Universe Sandbox
https://universesandbox.com/


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