Short answers, pulled from the story.
There were two main Celtiberian Wars. The First ran from 181-179 BC and the Second from 154-151 BC. Both were fought between Rome and a coalition of Celtic tribes in east central Hispania, including the Arevaci, Belli, Titti, Pellendones, and Lusones.
The Second Celtiberian War began when Rome objected to the Belli city of Segeda building a circuit of walls seven kilometres long and drawing in smaller surrounding towns. Rome argued this violated the peace treaties established by Tiberius Sempronius Gracchus after the First War. The Senate declared war and sent the praetor Quintus Fulvius Nobilior with nearly 30,000 men.
Tiberius Sempronius Gracchus ended the First Celtiberian War in 179 BC through a combination of military campaigns and diplomatic settlements. He introduced the vicensima, a five-percent grain tax collected directly by the state, and founded the settlement of Gracchurris in the Upper Ebro Valley, now Alfaro in La Rioja. His treaties were considered so fair that Celtiberian leaders sought their reinstatement when the Second War began.
At Numantia, seven kilometres north of modern Soria, the Roman general Nobilior deployed ten elephants against the city's defenders in 153 BC. When a stone struck one elephant, the animals stampeded through the Roman lines. The Numantines made a sortie and killed 4,000 Romans and three elephants, inflicting one of the war's worst Roman defeats.
Lucius Licinius Lucullus arrived as consul in 151 BC after Marcellus had already ended the Second Celtiberian War. He then attacked the Vaccaei, a tribe that had never fought Rome, without Senate authorization, crossing the River Tagus and massacring most of the roughly 20,000 inhabitants of Cauca. He was never called to account for the unauthorized campaign.
Publius Cornelius Scipio Aemilianus played two notable roles during the Celtiberian Wars. He volunteered for service in Hispania in the Senate when other officers were refusing to go, shaming reluctant recruits into enlisting. Later, during the siege of Itercatia, he accepted a single-combat challenge from an Itercatian horseman, won despite being smaller than his opponent, and lifted Roman morale during the deadlocked siege.