They work, oh yeah… well, sometimes.
I suppose that I should say that my bias is reflected from spending a lot of time growing up near the Mississippi, and doubting that we could really effectively control the whole flow of that massive body of water with a few levee’s. For the most part, they do work – and to reasonable effect. The downside is that too many people assume they’re foolproof and in my opinion don’t have enough respect for the power of the river. I spent some time myself doing sandbagging in the Flood of ’93 – but my respect for the sheer force of the river goes back a lot farther than that.
Rhonabwy 
I lived in Columbia during the 1993 floods and also spent time building a 3/4 mile long sandbag wall along the river facing edge of a small town.
These kinds of floods are like disasters in slow motion. “The river will peak 6 days from now”. You have six days to decide whether you want to pack up everything and get out, hope for the best, or build a sandbag wall that is hopefully high enough.
I watched houses lost because the sandbags were literally inches too short — the river crested 6 inches higher than forecast.
Vicious stuff, but the folks in these towns are tougher still. But even toughness can’t compete with the utter stupidity of the “flood control” projects that happened along the Mississippi and Missour rivers. Therein is the real problem in that they effectively eliminated large water buffers where floodwaters would effectively sit in a flood plain instead of all running downstream at once.
If it is this bad in Iowa and Northern Missouri now, Central and Southern will likely suffer in a few weeks, if the rain continues.
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