The question is simple:
What initiatives has Barack Obama done regarding the issue of torture and indefinite detention (as infamously done at Guantanamo Bay)?
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In regards to Guantanamo Bay Prison specifically, President Obama has been attempting to close it for several years. Various things have prevented it from being carried out. Wikipedia has a fairly good history of the closing attempts.
Some more recent news: http://www.guardian.co.uk/world/2013/jun/14/house-defense-bill-obama-guantanamo
In terms of torture, the issue is likely about 'enhanced interrogation'. The wikipedia page covers the various opinions on it. Pertaining specifically to Obama, the aforementioned wikipedia page mentions a few items. Two of them from the article:
There is also 'extraordinary rendition' which is "is the apprehension and extrajudicial transfer of a person from one country to another" and was allegedly used as a loophole to allow the interrogation of prisoners in countries that have lax torture regulations. Obama signed an executive order soon after taking office to put some tighter rules on the process.
Regarding indefinite detentions, he signed into law the NDAA last year and again this year with a clause allowing indefinite detention of anyone deemed a terrorist suspect. He has paid lip service to the disapproval of these provisions, but refused to actually exercise his power to veto either time until such provisions are removed.