A Little Question About Internet Hacking ?

Hello my fellow hackers, I have been scratching my head on this one and though I am not into it but would love to enhance my knowledge on the subject.

News are flying around with routers been hacked and I understand but then I notice, routers are hacked to patch the systems, others are hacked to install executable backdoors on the routers for later use. My question is how do hackers install backdoors since as far as I am concerned I cannot like get access to the router's low level interface except the normal 192.168.1.1 html interface. So how do they install backdoors to the router and upon every reboot still exists ? How are malwares also able to mitigate from one host to another ?

Any help would help since I own a router and I don't want to get hacked although I don't know if I have been hacked. ? I also want to experiment with my router.

Thanks in advance