My 4 yr old recently started waking up at 3-4am, and wanting to join me (and her father) in bed. How can I get her to sleep through the night?

Toddler not sleeping. Put her back in her bed every time she comes and gets in your bed. If you have to stay in her room briefly tell her a story.Make it up don't turn light on. When she settles down leave and go back to your bed. You have to be persistent. It may not be easy but don't give in. It is better for all of you that she sleeps in her own bed.
Tough love+ reward. I concur with the previous answers suggesting immediate return to her room. You can also offer her the promise of a reward for not doing so in the first place.Something simple like viewing a video (during the day) per successful night, and a trip to the toy store if she can stop for a week.After interrupting the pattern it should stop.
Get tough. Do not let her in your bed, even if you have to physically keep her out of the room. Make sure you have a good routine at bedtime and offer transitional items (doll, clock radio, nightlight) to help. If she has had a bad dream or is very upset, offer to go to er room for a short time and a few days at most.