The situation began on May 27th with the impending destruction of Taksim Gezi Park with the goal of increasing the width of a street. Concerned citizens began to gather at the site, forming a peaceful, non-violent demonstration against the construction project – a project that was pushed forward despite widespread disapproval and opposition.
The protesters had managed to halt construction until the following morning when the police intervened and protected the progression of the demolition operation. Sırrı Süreyya Önder, a member of parliament, in a Tiananmen Square Tank Man-like act, positioned himself in front of one of the bulldozers which, one again, halted the project. Before long, many had joined together to fight what Önder called an unauthorized and unlawful demolition project.
The police responded quickly, and with extreme force – in the early morning hours of May 30th they executed a raid on the site and began firing significant quantities of tear gas (learn more about the effects here) into the crowd. 
Despite excessive exposure to the chemicals, those involved in the demonstration were able to regroup and stand their ground. The following day (May 31st) two additional raids were conducted by police in their attempt to put an end to the assembly. As police continued to engage demonstration participants to prevent them from advancing through the area, many of the major routes into Taksim were inaccessible. Police continued to attack the protesters with repeated barrages of tear gas – more than once at frighteningly close ranges – and large water cannons.
After witnessing this response from their government, thousands of citizens made their way to Taksim Square to make their voice heard. Simultaneously, other protests began developing in other cities such as Ankara and Izmir – with others currently in planning. It was not long until people across the country decided to take a stand against the widespread and brutal actions taken against peaceful demonstrators desiring to assemble and exercise their rights. The violence affected everyone – even children and tourists found themselves caught in the overwhelming clouds of tear gas.
These demonstrations come without surprise. For some time, the people of Turkey have been growing displeased with authoritarian Prime Minister Tayyip Erdogan. 
His oppressive and violent acts against peaceful protesters at Gezi Park was the spark needed to ignite the fire. Reuters published that, “Hundreds of military officers have been jailed for plotting a coup against [Tayyip Erdogan] in recent years. Academics, journalists, politicians and others face trial on similar charges.” What began primarily as an environmental gathering has now developed into a stand against Erdogan. Mert Burge, a student in Turkey, said, “This isn’t just about trees anymore, it’s about all of the pressure we’re under from this government. We’re fed up, we don’t like the direction the country is headed in.”
In an effort to silence the demonstrators and place a curtain around what was taking place, the government appears to have disabled the tourist cameras that showed Taksim Square. NPR’s Peter Kenyon reported Tayyip Erdogan as saying, “The Taksim project will go ahead. If you bring 100,000, I’ll bring out a million.” Solidarity protests have been forming in cities throughout the world and more information on them is available here.
Amnesty International (AI) has released a statement (2013-05-31) stating, “The Turkish authorities must order police to stop using excessive force against peaceful protesters in Istanbul and immediately investigate alleged abuses, said Amnesty International after more than a hundred people were injured during an ongoing peaceful demonstration in a city centre park.” John Dalhuisen, Director of Europe and Central Asia Programme at Amnesty International, has said, “The use of violence by police on this scale appears designed to deny the right to peaceful protest altogether and to discourage others from taking part.” AI reports that their “activists who were observing the protest were also hit with truncheons and tear gassed.”
A document from 2013-05-03, released by Amnesty International, states the following: “May Day celebrations in Istanbul, Turkey were again marred by police violence and attempts by the authorities to prevent demonstrations from going ahead. Amnesty International is concerned that once again police used excessive force against demonstrators, including the widespread and excessive use of water cannon and tear gas against peaceful protestors.”
Human Rights Watch (HRW) has released a statement (2013-06-01) that, “Prime Minister Recep Tayyip Erdoğan’s government should end police violence and excessive use of force against protests across Turkey. Officials should uphold the right to peaceful protest and free speech.” Emma Sinclair-Webb, a senior Turkey researcher for the organization has said, “The Turkish authorities should urgently review policing policies and hold to account police chiefs whose units attacked peaceful protesters. The government should also examine police use of tear gas, which poses a significant health risk and can be lethal.” HRW, in December 2008, analyzed police violence in Turkey. Their findings are detailed in an 80-page report located here.
Perhaps the most powerful information on the events comes from Twitter, YouTube, and Facebook: Memento Mori uploaded an incredibly powerful 90 second video to Vimeo, available here: http://vimeo.com/67432788
YouTube user ocannal uploaded a video of a Turkish protester being hit by a police panzer:
I discovered this photo on Twitter from @Brclne –
This image, which I discovered from @HandeVaro1, shows a man bleeding profusely from his head (I don’t know anything more about him):
@emregecer shared this image of demonstrators gathering en masse:
Protesters are being hit with what appears to be expired tear gas:
This video reveals some of the harsh attacks committed by the police:
Across Istanbul, support for the demonstrators is being shown with flashing lights, horns, and the clanging of pots and pans:
And demonstrators refuse to be discouraged (from Instagram user irmszr):
And from Instagram user nenbereth:
Other perspectives on the situation can be found here:
Why the Gezi Park Protests Do Not Herald a Turkish Spring (Yet)
The Right to the City Movement and the Turkish Summer
Occupy Gezi Protest: Erdogan Defiant As Police And Protesters Clash
Notes:
1. The most popular Twitter hashtag for the situation is #OccupyGezi
2. Some are claiming that “Agent Orange” is being used against protesters – this is unconfirmed and unlikely.
3. The seemingly de facto official Facebook page for the movement is located here.
Update 12:40 AM 2013-06-02: Read a conversation I had with Zehra, a member of the OccupyGezi movement.