When I first moved into my apartment I had mad problems with mice. I titled my place as mice central. I didn't know how they were getting in and I must have trapped a dozen of these things in the beginning.
Moving was not an option for various reasons and the super here is very lazy and the owners very tight w/ money.
So my attitude was to hell w/ waiting for someone to do something while I'm living w/ the pest.
You got to look high and low for openings anywhere in your apartment. I was surprised what I found. My apartment had 2 inch spaces above and below each window! I found this out after actually watching a mouse scurry for cover then climbed up my speaker wire onto the opening under the window. I got plaster for that and filled it in. I later realized after getting a good amount of fruit flies and regular flies in my apartment even when a door or window wasn't cracked that the 2 inch space above the window allowed them to come in.
After getting a hold on the mice problem I suspected they were still getting in and couldn't figure it out and by this time the roach problem began.
When I first moved in I hardly saw one then it began to increase even w/ using boric acid. Boric acid helps only to an extent. I caulked every wall boarder once I discovered an 1/8 inch opening where the floor didn't meet the floor board. Before caulking I used to put boric acid in the gap but found a few roaches were killed but many just walked through it.
O'k, no more mice droppings but find places where mice urine was left. Roaches cut down a lot but I didn't want to see a one.
Found cracks and openings in the oddest places like in my closets. Holes were just above the door joint right on the inside of the door. Holes were also around the shelving that weren't visible looking eye level. I also used a mirror in places I didn't have a clear view.
Sorry for the long post but just trying to help you. You have to cover every inch of your apartment. Get on a step stool and look, use a flashlight or lamp, get on the floor and really take a close look at the floorboards. Take a very close look. One of the early mistakes I made was thinking nothing could get in some of the spaces I found until one day after I chased down a roach in my kitchen it slipped behind the cabinet that was flush to the wall. I thought not even a slip of paper could get between there but an adult roach did. I caulked all around the cabinets, windows, doors, electrical box, you name it I caulked.
Now I can go days without seeing a roach. Any that I've seen I quickly kill. I pour bleach down my drains at night since they can come up that way. I have roach baits in every area where they used to be. I sprayed insulating foam all around the radiator valve where roaches and mice used to come up.
I haven't seen or heard evidence of mice either.
None of this was easy but I was determined not to live with the bastards.
Use caulk, steel wool (if you have mice), and plaster. I swear by the Combat Platinum Roach baits. As others have said get behind the stove, refrigerator--spray and put roach baits there, caulk and fill holes under sinks. Keep water and dishes out of the sink and make sure you keep it dry. Although just being clean isn't enough to keep roaches away you have to keep clean. Roaches can feed on the smallest crumb. Small roaches feed on the adult fecal matter and anywhere you see that this is were they'll congregate. So you have to make sure you clean and wipe with bleach all roach poop.
You can find out they're paths by using the sticky traps.