In distributed averaging and consensus algorithms, processors exchange and update certain values (or "estimates", or "opinions") by forming a local average with the values of their neighbors. Under suitable conditions, such algorithms converge to consensus (every processor ends up holding the same value) or even average-consensus (consensus is achieved on the average of the initial values held by the processors). Algorithms of this type have been proposed as a subroutine of distributed optimization methods, used to combine the results of different processors while a master algorithm is running. We overview a few applications of averaging algorithms, with a focus on gradient-like optimization methods. We then proceed to highlight some results, old and new, with a focus on convergence rates. We finally discuss some open problems.