Maj. Gen. Samuel R. Curtis, USA
Maj. Gen. Earl Van Dorn, CSA

Casualties were heavy, with roughly 4,600 Confederates falling and 1,400 Northerners.

The Confederates were eager to return to Missouri so that its star on their flag would have real meaning.  Meanwhile, Lincoln wanted to hold as many Border States in the Union as possible.  The verdict of battle at Wilson's Creek in the summer of 1861 had favored the south, but when General Samuel R. Curtis was appointed he restored Union fortunes.  Reinforced, and more active than his predecessor John C. Fremont (a political general if there was one) he'd not only secured Missouri, he'd pushed down into northwest Arkansas.

Sterling Price and Ben McCulloch had proved disappointments the previous year, and there was a further reason not to promote either one: they detested each other, and if one was promoted some of the other's men would desert.  So Jefferson Davis dipped into his limited stock of diplomacy (he was a prickly man) and in the early spring of 1862 appointed a new commander: Earl van Dorn.  Van Dorn was an aggressive man, with a good reputation for his work in the Manassas campaign.  He worked hard on his new command in the few days he allowed himself, and tried to meld Price's Missourians with McCulloch's Texas-Arkansas contingent - and to add the wild card of Albert Pike's 800-odd pro-Confederate Indians.

Van Dorn was eager to attack the Yankees, and he rode hard for two days to join his command, catching a fever in the wintry valleys of northern Arkansas.  His plan was relatively simple: advance soon, while the Union forces were scattered in winter quarters, win whatever battles were necessary and create momentum that would take him "Huzza for St. Louis". 

But the first step was to win the first battle, and it would be hard, despite his 3:2 numerical advantage over Ryan's 10,000 men.  Van Dorn faced a difficult task: he had to attack a competent enemy in constricting terrain, where the Confederate's superiority in numbers would matter less.  To make things worse, Ryan had picked a strong position, on a small ridge overlooking a stream with marshy flanks.  Van Dorn took a look at it and knew no frontal attack could succeed.

So he revised the plan, now intending to outflank the Federals and fall on their unprotected rear by a two-pronged night march.  He would win the battle thanks to numbers and surprise, then Ryan would have nowhere to retreat and van Dorn would capture the Union remnants.  It was not a bad plan, and his opening move was excellent: he left campfires burning and deceived Ryan about the Confederate plan.  The night march got a bit chaotic, and some units didn't turn up where they were intended, and even more were late, which gave Curtis time to redeploy a bit.
More important, Curtis didn't lose his nerve.  He held the smaller Confederate force, McCulloch's men coming from the west, with a cavalry screen.  It didn't last long, and a combined Cherokee-cavalry charge routed the Union horsemen.  But McCulloch couldn't maintain the momentum, and by the time he could again bully his men forward the Yankees had a defensive line.  McCulloch, a former Texas Ranger worshipped by his men, was killed leading a charge; his second-in-command fell soon after, and the third-in-command was captured.  The Confederates didn't know who would take over, and Albert Pike, the eventual choice, inspired few.  This part of the battle ebbed to an end, neither side able to take advantage of the other's fatigue and confusion.

The main Southern force, with Price and the sick Van Dorn (he tried to command from an ambulance) ran into stronger Union forces, under a hard-bitten Regular, Eugene Carr.  The Confederates used their artillery well, and pushed Carr back through successive defensive lines, but never took many prisoners: the Union troops kept their cohesion and kept on fighting.  It was an ominous sign for the tired, ill-supplied Confederates (to move faster on his flank march Van Dorn had sent most of the supply wagons back to his base) and as the late-winter sun sank the battered Union line was still intact near the Elkhorn Tavern.

What cold van Dorn do the next day?  He hoped that Ryan's men were damaged and discouraged enough that they'd surrender.  But if they didn't van Dorn was the one in trouble: his men were tired, short of food and ammunition.  Worse, the forces were separated, the two Confederate columns (Price's and formerly McCulloch's) had the Union army in between.  Ryan didn't budge (despite gloomy advice from some of his subordinates overnight), and when the dawn came his men were still in the middle of the two Confederate forces.  Ryan had also brought up his reserve, the two fresh divisions of Sigel's force.

Pike's men (formerly McCulloch's) stayed quiet, tying down some Union forces to the west of Elkhorn Tavern.  The tables on the northern flank were turned: Ryan had more and better artillery, with plenty of ammunition.  He had more infantry, and morale was high.  Van Dorn staked all he had left on an impressive opening show, and he began bombarding the Union lines.  But his guns were soon smothered by the superior Union artillery, which first battered the Confederate guns, then turned on the grey-clad infantry.  Once the guns had prepared the way, Sigel's men charged, and the Rebel lines broke.  Carr's and Davis' divisions joined the advance, and Van Dorn's army melted away.  Casualties were heavy, on paper: 1,400 Federals and 4,600 Confederates, although many were deserters rather than battle casualties.  Still, they would not be fighting for the South and that was what mattered.

Few of the 4,600 were captured, but the South had to abandon plans to invade Missouri.  Instead, Ryan was secure in northern Arkansas, while the Southern forces were dispersed to regions more immediately threatened.  Price wouldn't return to Missouri until mid-1864, by when it was too late.