Nowadays the built-in Android browser has been replaced by Chrome, which does this perfectly well. You can long-press and save virtually any image or link, and even videos from a number of sites that couldn't be easily done on the desktop.

Answer below for older devices:

The Android browser by default can only download files that the Android system "recognizes" (i.e., there has to be a program registered to handle that file type). It's a stupid restriction in my opinion, but you can install Download Crutch to overcome this limitation (it registers itself for every filetype).

If you're referring to images that link to something else and you want to save the something else, long-press on the image and choose "Save Link As" or similar.

Use https://pub.dartlang.org/packages/flutter_downloader. Don't forget to do platform configurations.

Basically, this is how you should use the package. There is a detailed long example in the link.

final taskId = await FlutterDownloader.enqueue(
  url: 'your download link',
  savedDir: 'the path of directory where you want to save downloaded files',
  showNotification: true, // show download progress in status bar (for Android)
  openFileFromNotification: true, // click on notification to open downloaded file (for Android)
);

Edit: Some people said the package on top is not well maintained. Try this one https://pub.dev/packages/flowder

How to download file from Url

fun downloadPdf(baseActivity:Context,url: String?,title: String?): Long {
        val direct = File(Environment.getExternalStorageDirectory().toString() + "/your_folder")

        if (!direct.exists()) {
            direct.mkdirs()
        }
        val extension = url?.substring(url.lastIndexOf("."))
        val downloadReference: Long
         var  dm: DownloadManager
         dm= baseActivity.getSystemService(Context.DOWNLOAD_SERVICE) as DownloadManager
        val uri = Uri.parse(url)
        val request = DownloadManager.Request(uri)
        request.setDestinationInExternalPublicDir(
                "/your_folder",
                "pdf" + System.currentTimeMillis() + extension
        )
        request.setNotificationVisibility(DownloadManager.Request.VISIBILITY_VISIBLE_NOTIFY_COMPLETED)
        request.setTitle(title)
        Toast.makeText(baseActivity, "start Downloading..", Toast.LENGTH_SHORT).show()

        downloadReference = dm?.enqueue(request) ?: 0

        return downloadReference

    }

Bofore calling this method do check for Runtime permission:

Manifest.permission.WRITE_EXTERNAL_STORAGE

Using Async task

call when you want to download file : new DownloadFileFromURL().execute(file_url);

public class MainActivity extends Activity {

    // Progress Dialog
    private ProgressDialog pDialog;
    public static final int progress_bar_type = 0;

    // File url to download
    private static String file_url = "http://www.qwikisoft.com/demo/ashade/20001.kml";

    @Override
    public void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);

        setContentView(R.layout.activity_main);

        new DownloadFileFromURL().execute(file_url);

    }

    /**
     * Showing Dialog
     * */

    @Override
    protected Dialog onCreateDialog(int id) {
        switch (id) {
        case progress_bar_type: // we set this to 0
            pDialog = new ProgressDialog(this);
            pDialog.setMessage("Downloading file. Please wait...");
            pDialog.setIndeterminate(false);
            pDialog.setMax(100);
            pDialog.setProgressStyle(ProgressDialog.STYLE_HORIZONTAL);
            pDialog.setCancelable(true);
            pDialog.show();
            return pDialog;
        default:
            return null;
        }
    }

    /**
     * Background Async Task to download file
     * */
    class DownloadFileFromURL extends AsyncTask<String, String, String> {

        /**
         * Before starting background thread Show Progress Bar Dialog
         * */
        @Override
        protected void onPreExecute() {
            super.onPreExecute();
            showDialog(progress_bar_type);
        }

        /**
         * Downloading file in background thread
         * */
        @Override
        protected String doInBackground(String... f_url) {
            int count;
            try {
                URL url = new URL(f_url[0]);
                URLConnection connection = url.openConnection();
                connection.connect();

                // this will be useful so that you can show a tipical 0-100%
                // progress bar
                int lenghtOfFile = connection.getContentLength();

                // download the file
                InputStream input = new BufferedInputStream(url.openStream(),
                        8192);

                // Output stream
                OutputStream output = new FileOutputStream(Environment
                        .getExternalStorageDirectory().toString()
                        + "/2011.kml");

                byte data[] = new byte[1024];

                long total = 0;

                while ((count = input.read(data)) != -1) {
                    total += count;
                    // publishing the progress....
                    // After this onProgressUpdate will be called
                    publishProgress("" + (int) ((total * 100) / lenghtOfFile));

                    // writing data to file
                    output.write(data, 0, count);
                }

                // flushing output
                output.flush();

                // closing streams
                output.close();
                input.close();

            } catch (Exception e) {
                Log.e("Error: ", e.getMessage());
            }

            return null;
        }

        /**
         * Updating progress bar
         * */
        protected void onProgressUpdate(String... progress) {
            // setting progress percentage
            pDialog.setProgress(Integer.parseInt(progress[0]));
        }

        /**
         * After completing background task Dismiss the progress dialog
         * **/
        @Override
        protected void onPostExecute(String file_url) {
            // dismiss the dialog after the file was downloaded
            dismissDialog(progress_bar_type);

        }

    }
}

if not working in 4.0 then add:

StrictMode.ThreadPolicy policy = new StrictMode.ThreadPolicy.Builder().permitAll().build();
StrictMode.setThreadPolicy(policy); 

Download File from URL

There are a couple ways to do this. As mentioned, using the developer tools could work (more likely it will give you the url to the file) and right-clicking the link will work. Alternatively there are these options.

In Chrome

1. Go to the URL
2. Right-click the webpage
3. Select Save As...

For verification purposes, here are png, jpg, and mp3 links. Follow them and try these steps. However, in my experience. If you already have a url to a file, opening up Chrome and following these steps is rather tedious so here is an alternative.

In Command Line

1. Open your favorite terminal emulator
2. type curl -O URL

• Where O is written in capital
• And URL is the URL to the file, e.g. http://example.com/file.mp3

I have seen something like this before, can't remember what though. I'll look for it.