The siege of Olynthus (early 479 BC) was a success for the Persian forces that had escorted Xerxes back to the Hellespont after the battle of Salamis and saw the city fall to assault and a large part of its population massacred.
Olynthus was located at the head of the Gulf of Torone, which sits between the west and central of the three peninsulas of Chalcidice (Pallene to the west and Sithonia in the middle). At the time of the siege the city was ruled by the Bottiaeans, a Thracian tribe that had been driven east by Alexander I of Macedon.
The siege can be placed roughly at the end of 480 or the very start of 479 BC. The battle of Salamis was fought in late September 480. Once Xerxes decided to return to Asia the journey took 45 days, taking us to the middle of November 480 at the earliest. His escort then turned back and headed back towards Thessaly. If we allow another two weeks for the trip back to Chalcidice this brings us to the start of December 480. The siege of Potidaea, which was being conducted at the same time, lasted for three months. Olynthus fell during the siege of Potidaea, so probably early in 479.
In the aftermath of Salamis Xerxes decided to leave 300,000 men under his brother-in-law Mardonius to over-winter in Thessaly and complete the conquest of Greece in the following year. Xerxes then returned to Asia overland with the rest of his army, and 60,000 men from Mardonius's force (a sign that the quality of the rest of the army may not have been very high). This force was commanded by Artabazus, son of Pharnaces, one of his better generals.
During the return trip to Thessaly Artabazus discovered that the people of Pallene had revolted against Persian control. He decided to lay siege to Potidaea, the city at the narrow northern tip of the peninsula. He also suspected that Olynthus supported the revolt, and decided to attack that city as well.
Potidaea successfully resisted the Persians for three months and that siege was eventually lifted. The people of Olynthus weren't as lucky. Artabazus was able to force them to surrender. According to Herodotus he then massacred the Bottiaean part of the population in a lake near the city. Control of the city was then handed over to Critobulus of Torone (a city towards the southern end of Sithonia), showing that not all Chalcidians had supported the revolt against Persian authority.
Potidaea was much harder to besiege. It sat across the narrow northern tip of Pallene, blocking access to the peninsula. After the fall of Olynthus the Persians concentrated on the attack on Potidaea, but suffered heavy losses during what appears to have been a tsunami. After that Artabazus lifted the siege and returned to Mardonius's camp in Thessaly.