How do you transport your baby when you're out and about?

If you're out and about with your baby, say running errands, how do you bring your baby with you? Do you put their car seats in the strollers or do you take them out of the car seat and wear them? Would love to hear some experiences- my baby always wakes up in her car seat and won't stop crying - I'm debating if I should carry her in a wrap when I'm out.