In addition to @Fujia response, I wanted to add an example. This is the method I have been using recently for posting png files:
func WasperEntrepriseImageUploadCall(method: Alamofire.Method, imageData: NSData, parameters: [String: AnyObject]?, headers: [String: String]?, urlToPost: String, 
    progressionHandler: (bytesWritten: Int, totalBytesWritten: Int, totalBytesExpected: Int) -> (), 
    completionHandler: (NSURLRequest?, NSHTTPURLResponse?, Result<AnyObject,NSError>, NSData?) -> ()){
    Alamofire.upload(
        method, urlToPost, headers: headers,
        multipartFormData: { multipartFormData in
            multipartFormData.appendBodyPart(data: imageData, name: "file", fileName: "doesntmatter", mimeType: "image/png")
            if let params = parameters{
                for (key, value) in params {
                    multipartFormData.appendBodyPart(data: value.dataUsingEncoding(NSUTF8StringEncoding)!, name: key)
                }
            }
        },
        encodingCompletion: { encodingResult in
            switch encodingResult {
            case .Success(let upload, _, _):
                upload.progress { bytesWritten, totalBytesWritten, totalBytesExpectedToWrite in
                    progressionHandler(bytesWritten: Int(bytesWritten), totalBytesWritten: Int(totalBytesWritten), totalBytesExpected: Int(totalBytesExpectedToWrite))
                }
                upload.response { response in
                                          }.validate()
                    .responseJSON { response in
                        if let resp = response.response{
                            print(resp.statusCode)
                            print(response.result.value)   // result of response serialization                          
                        }
                        completionHandler(response.request,response.response,response.result, response.data)
                }
            case .Failure(let encodingError):
                print(encodingError)
            }
        }
    )
}
Not the best solution, but it should give you a head start. Requires both SwiftyJSON and Alamofire 3.0 I believe. Gives you a completion handler for progress which can be useful. You should be able to find a more detailed answer here : Uploading file with parameters using Alamofire