Bikes are great, but carrying cargo / groceries /etc. is a serious problem.
I have an exotic Xtracycle project that lingers in my bike workspace. It's a bolt on sub frame that extends the bike length to about the rough size of a Harley dressed up motorcycle. With the Xtracycle you can tow 250 pounds and it has sidebags and I have the bottom cargo slings for strapping boxes down and bulky stuff. I've done beer runs on it. Works best with two cases balanced on each side. Yeah, mine is many years old and not the odd stuff on their site now
http://www.xtracycle.com/
Oh yeah, that bike has a gas motor which I get 350 MPG out of and it does 35MPH and climbs mountains. Now to get it to stop breaking spokes --- it's a direct drive belt setup. Bunch of other custom work on that bike too. Custom mounts, handlebar expansion bar for accessories, dual fuel can mounts (camping fuel bottles in dual water bottle cages), etc.
My city commuter has a kid style bike trailer I take out when heading to farmers market. The trailer actually is chromolly (steel) and has a hard back seat that folds into a flat surface for boxes and things. Pretty alright for an throwaway. Had to improvise with the mount though since it was long gone / missing.