There were many sailing ships fitted with auxiliary steam power on the oceans from the time of the Savannah in 1819, and the somewhat controversial interpretations of the voyages of the Curacao in the late 1820`s. But, true transatlantic steamship travel begins in earnest in 1838 when the Great Western and the Sirius run a race from England to New York. The Great Western started four days behind the Sirius and arrived only hours later. The Great Western was the first ship designed specifically as a transatlantic passenger vessel built to use primarily steam power. She was a side wheeler. The Sirius, also a side wheeler, had actually been designed as a steamer to cross the channel, but was pressed into transatlantic service as a publicity stunt. It is said that she burned her cabin furniture, spare yards, and one mast in the effort to win the race. The ships belonged to two companies competing for the new Atlantic steam passenger business.
The next advances in steamship power were double and triple expansion engines where the steam exhausted from one cylinder powered another. Such engines were soon powerful enough to power screw propellers, the Great Britain was the first “steam screw” in 1845. Developed right around the turn of the 20th Century, steam turbine engines when added to screw propellers were the height of steamship technology. The Titanic, and her sister ships the Britannic and the Olympic were steam ships built in the early Twentieth Century. Although everyone knows that the Titanic met with disaster on her maiden voyage she really was an engineering marvel.
So also was the Queen Elizabeth built with steam turbine engines and screw propellers in the mid 20th Century. As was the Queen Elizabeth II when first built in 1969, although she was later converted to diesel-electric. Steam screws stayed in use for a surprisingly long time, but most new ships now being built have diesel engines tied to electric generators which drive electric motors tied to the propellers.