Swift blocks not working

It has something to do with how Swift implement closure. You need to use @convention(block) to annotate that the closure is ObjC block. Use unsafeBitCast to force cast it

var block : @convention(block) (NSString!) -> Void = {
   (string : NSString!) -> Void in 
    println("test")
}

ctx.setObject(unsafeBitCast(block, AnyObject.self), forKeyedSubscript: "test")

from REPL

swift
Welcome to Swift!  Type :help for assistance.
  1> import Foundation
  2> var block : @convention(block)(NSString!) -> Void = {(string : NSString!) -> Void in println("test")}
block: @convention(block)(NSString!) -> Void =
  3> var obj: AnyObject = reinterpretCast(block) as AnyObject
obj: __NSMallocBlock__ = {} // familiar block type