Roaches can get inside your home easier than you may want to believe. The most common ways include the following:
Cracks and crevices. Like many other kinds of pests, roaches make their way indoors from your yard by squeezing through openings around your doors and windows.
Plumbing fixtures. An especially common occurrence in multi-family housing, roaches are sometimes found moving from unit to unit through plumbing systems. This is often seen with Oriental cockroaches.
Groceries. German and brown-banded roaches are the most common kind of cockroach found in grocery bags. They can easily sneak into your home from an infested environment without your knowledge.
Sewers or drains. Similar to plumbing, sewer systems are a common avenue for American cockroaches to infest homes through. Use steel wool or screens to block off gaps that they would be able to crawl through.