prodirati

1. (of light, water, cold) to penetrate; to seep in
   Voda prodire u podrum svaki put kad pada kiša. — Water seeps into the basement every time it rains.
   Svetlost prodire kroz tanke zavese. — Light comes through the thin curtains.
2. (of troops, a crowd) to break through; to advance
   Neprijateljska vojska prodire ka gradu. — The enemy army is advancing on the city.
3. (of a company, an idea) to make inroads; to penetrate
   Kineski automobili sve više prodiru na evropsko tržište. — Chinese cars are increasingly making inroads into the European market.
4. (of understanding, knowledge) to gain a deeper understanding of; to get to the heart of
   Učenici treba da prodiru u suštinu problema, a ne da uče napamet. — Students should get to the heart of the problem rather than learn by rote.

Usually with «u» or «kroz» + acc.; the perfective is prodreti.