An example of how you can use the error handling in Swift 2.0 for an asynchronous API.

AsynchronousThrow.swift

typealias EmptyResult = () throws -> ()
typealias AsyncResult = (EmptyResult) -> ()

typealias JsonResult = () throws -> JSON
typealias AsyncJsonResult = (JsonResult) -> ()

class GetResponse {
    
    func main() {
        
        Response.updateAsync { result in
            do {
                // Call the result to let it try to throw an error
                try result()
            } catch {
                print(error)
            }
        }
        
        Response.getAsyncResult { jsonResult in
            do {
                // Call the result to let it try to throw an error
                let json = try jsonResult()
                // Use `json` as usual
            } catch {
                print(error)
            }
        }
    }
}

class Response {

    // Asynchronous empty response
    class func updateAsync(result: AsyncJsonResult) {
        Async.background { error in
            if let error = error {
                // Create result block that throws an error
                result { throw error }
                return
            }
            // Create result block that doesn't throw anything
            result {}
        }
    }
    
    // Asynchronous JSON response
    class func getAsyncResult(result: AsyncJsonResult) {
        Async.background { json, error in
            if let error = error {
                // Create result block that throws an error
                result { throw error }
                return
            }
             // Create result block that return the json
            result { json }
        }
    }
}