Motorola != Motorola Mobility. Motorola Mobility is a recent spin-off from Motorola and encompasses the original company's handset business as well as its related patent portfolio.
What does Motorola do? Well ... cellular infrastructure is their core business, and they also have services/solutions for things like emergency response services (e.g. 911 in the US), law enforcement, and I think they still make walkie talkies.