Do aircraft maintenance technicians work for airlines, airports, or a different business entirely?

Yes, you can work in an airlines company and ground aircraft support in the airport. But you need your A&P Certification FAA first. You can work also in the Formula One race cars, because they have turbine engines, but you need your FAA A&P Cetification.
Good luck.

Hello Landon, with major airlines, they normally hire their own technicians. They often look for students fresh out of a A&P licensing school. We always use to say that an airline did not want someone with a load of experience. They would rather guide them with additional training on the job. However, there are exceptions when an individual would be hired after their military service. That may be with 14 years or even 20 years of service. Today you would definitely want to obtain a license and even some avionics training would be beneficial. Along with a decent salary you would have great benefits.
There are also repair centers around the country. They are not airlines but do service and repair aircraft for airlines and leasing companies. They do offer opportunities for individuals with less pre-training which means the salary can be a third less or even more. I am not a fan of these facilities from an employee viewpoint.

I would suggest you take the path with a major airline, get the A&P license, and a local community college would offer the avionics course.

Hello Landon,
I have been in aircraft maintenance for 26 years, and loved every minute of it. I got my FAA Airframe and Powerplant license in high school, then went to college and earned my Bachelors degree. I started as line service/baggage handler, and started talking to the mechanics. One day, one of them asked me give him a hand with a small task. The technician was happy with my performance and once I mentioned that I have my A&P, he dragged me to his manager and gave me a recommendation. I had to take a drug test and a 10 background check and was officially hired as a technician.
Every company has different hiring techniques, but almost all will administer a drug test and a 10 year background check. Some will perform a phone call screening, then call you in for an interview. Some will call you in for multiple interviews, while others will just have multiple people in the room asking questions at the one interview. Recommendations go a long way to getting your foot in the door, a lot of times its who you know and not what you know.
As a hiring manager, I will review the applications and narrow it down to a few. I do ask my supervisors if they have heard of or know any of the applicants. You will be surprised how many times someone knows some else. I can call some of the past employers and ask for references, it always helps to leave on good terms. If the applicant is not local, I will conduct a phone call screen, and if it all works out so far, I will call you in for a face to face interview. I only have a few minutes to make an opinion of weather you are going to fit in my organization. Your resume will let me know what your experience and level of expertise should be, and again, I only have a few minutes to evaluate if your resume is real or just fluff. I may ask weird questions just to see how you respond. Pending on the position I may ask you "On a scale of 1 to 10, how weird are you?". If you are a 10, you may be psychotic, but if you are a 1, you may be too boring and unimaginative, again its just to see how you react and handle the unpredictable. If I ask you on a scale of 1 to 10 how good a mechanic are you, and you answer 10, I will expect you to walk on water to get to my airplane.
Interviews should not be stressful, its a time to get to know each other. I am interviewing you, but you are interviewing me as well. Be honest and ask questions. Prepare some questions ahead of time. Don't be quick to ask about the salary, that time will come and you don't want me to think that you are only here for the money. Its about the fit, make sure you want to be there, as much as they need you there.
Good luck, hope this helped.

Generally in the larger companies mechanic's work directly for the airline at most locations. There are many locations where these services are contracted out to another business. Both scenarios have pros and cons.

I started as an avionics technician for the USAF on these really old airplanes F-4Es any Gs. Best job I ever had! Between working in the shop and the flight line I earned two AA degrees and a BS in Electronics. As I was departing my 4 year hitch, I filled out one application and was hired.

Yes the USAF did a background check and so does every other employer these days. Through the years I had attained a Top Secret clearance based on the assignments I was given. All I can say is: Always disclose everything, they will sort out the truth no matter what. Honesty is the only way.

Today, it seems rare to have only one interview with one person. Usually now most companies perform structured interviews with panels, standard questions. I don't think either the "one on one" or "the panels" are strenuous. Consider they are looking for you, they are hoping you are the one because they really don't want to keep the process going any longer than they have to.