In an age when checks can be deposited by smartphone and almost everyone retrieves cash from ATMs, the corner bank can seem a relic, with its paper deposit slips, marble countertops and human tellers behind glass partitions.

But some banking executives say the brick-and-mortar branch is still the best way to serve existing customers and snag new ones. They’re trying to rebuild the nation’s neighborhood banks into hip, airy spaces where customers sign up for loans without touching a piece of paper, sign in to ATMs with a tap of their smartphones and talk to off-site tellers by video.