Alexander crossed the Indus in 326 BCE and fought Porus, Paurava, on the Jhelum at a place the Greeks called the Hydaspes. He won and reinstated Porus as a subordinate ruler, which is unusual enough to be remarked on in every account.
He founded two cities on the river, Nicaea and Bucephala, the latter named for his horse, which died there. Neither has been located with certainty.
He fought his way down through the Punjab against the Malloi, probably around Multan, where he was severely wounded in an assault on a citadel.
At the Beas his army refused to go further. He turned south and went down the Indus to the sea and then west through Gedrosia, where a large part of his force died.
The Greek accounts are the earliest external descriptions of this region: the crops, the rivers in flood, the elephants, the cities, the philosophers who argued with him.
No site of any of it has been identified beyond dispute. An invasion that produced a library of ancient literature left almost nothing on the ground that anyone can point to.
Arrian, Curtius, Diodorus, Plutarch and Justin are the surviving accounts and every one of them is late, written between three and five centuries afterward out of sources that are lost. What they preserve of Ptolemy, Nearchus and Aristobulus is at second hand, and they disagree with each other on nearly every number in the story.
The Jhelum has moved. The crossing was at a ford somewhere above the modern town, and since the river has changed course repeatedly in two thousand three hundred years the search for the place has been an argument about old channels rather than a matter of digging.
He left garrisons and cities behind him and none of them held. What survived was a Hellenistic presence in the north west that produced the Indo-Greek kingdoms and, later, the Gandhara sculpture.