Erastus - see the notes on Romans 16:23.
Abode at Corinth - This was his home, where he filled an important office; see the notes at Romans 16:23. It would seem that when Paul went to Rome, there was some expectation that he would accompany him, but that reasons had occurred for his remaining in Corinth. His doing so is referred to without blame.
But Trophimus - see Acts 20:4. He was a native of Asia Minor.
Have I left at Miletum sick - Probably he designed to accompany him to Rome, as he had been often with him in his journeys. On the situation of Miletus, or Miletum, see the notes on Acts 20:15.

Erastus abode at Corinth - He was treasurer of that city, as we learn from Romans 16:23 (note). The apostle had sent him and Timothy on a mission to Macedonia, Acts 19:22, whence it is probable he returned to Corinth, and there became finally settled.
Trophimus have I left at Miletum sick - Even the apostles could not work miracles when they pleased; that power was but rarely given, and that for very special purposes. Trophimus was an Ephesian. See Acts 20:4, and the note there.
Miletus was a maritime town of Ionia, not far from Ephesus; but there was another Miletus, in Crete, which some learned men think to be intended here. It appears that St. Paul went from Macedonia to Corinth, where he left Erastus; from Corinth he proceeded to Troas, where he lodged with Carpus: from Troas he went to Ephesus, where he visited Timothy; from Ephesus he went to Miletus, where he left Trophimus sick; and having embarked at Miletus, he went by sea to Rome. See Calmet. It is most likely, therefore, that the Miletus of Ionia is the place intended.

Erastus abode at Corinth,.... He was chamberlain of that city, Romans 16:23 who being sent along with Timothy into Macedonia, Acts 19:22 very probably went from thence into Achaia, to Corinth, his native place, where he stayed.
But Trophimus have I left at Miletum sick. Trophimus was an Asian, of the city of Ephesus, the same that is spoken of in Acts 20:4. Some say he suffered martyrdom the same day the Apostle Paul did; but others say, that after that time he was bishop of Arles in France. This man went with the apostle into Asia, and from thence to Jerusalem, and came along with him in his voyage to Rome, but falling sick by the way, was left at Miletum. Some, instead of Miletum, would read Melita, that being the island Paul, and the ship's company, escaped to, when they were shipwrecked, Acts 28:1 here it is supposed Trophimus was left sick. Others have observed, that there was a city called Miletus in the island of Crete, under which Paul sailed, Acts 27:7, see footnote (j), and is the place intended; but there is no need to suppose either of these; no doubt Miletum, near to Ephesus, is meant; and as the apostle sailed by the coast of Asia, Acts 27:7, on which shore Miletum was, there is no difficulty in supposing him put ashore there. The Alexandrian copy reads "Melotus".
(j) Plin. l. 4. c. 12.

In order to depict his desertion, he informs Timothy that Erastus, one of his usual companions (Acts 19:22, possibly the same Erastus as in Romans 16:23, though how he could leave his official duties for missionary journeys is not clear), stayed behind at Corinth, his native place, or usual residence, of which city he was "chamberlain," or city steward and treasurer (Romans 16:23); and Trophimus he left behind at Miletus sick. (On his former history, see on Acts 20:4; Acts 21:29). This verse is irreconcilable with the imprisonment from which he writes being the first: for he did not pass by Corinth or Miletus on his way to Rome when about to be imprisoned for the first time. As Miletus was near Ephesus, there is a presumption that Timothy was not at Ephesus when Paul wrote, or he would not need to inform Timothy of Trophimus lying sick in his immediate neighborhood. However, Trophimus may not have been still at Miletus at the time when Paul wrote, though he had left him there on his way to Rome. Prisca and Aquila were most likely to be at Ephesus (2-Timothy 4:19), and he desires Timothy to salute them: so also Onesiphorus' household (2-Timothy 1:18). Paul had not the power of healing at will (Acts 19:12), but as the Lord allowed him.

When I came on, Erastus abode at Corinth - Being chamberlain of the city, Romans 16:23. But Trophimus I have left sick - Not having power (as neither had any of the apostles) to work miracles when he pleased, but only when God pleased.