Actually, developers should port their libraries to Maven or Google. In this case, jCenter() can be removed from Gradle.

A problem occurs when old libraries are no longer maintained or the developers are retired.

There are only two possibilities:

a) search e.g. in Maven for a similar library.

b) Download the corresponding source code from GitHub and create your own local library from it.

As of 2022-02-01 JCenter is definitely down.

Please see the new answer.

Summary: After February 1st, 2022 jcenter() will not work anymore.

According to this Gradle blog post:

Gradle 7.0 will deprecate the use of jcenter() to resolve dependencies.
You will still be able to use JCenter as a repository, but Gradle will emit a warning.
The jcenter() method will be removed in the next major release.

Gradle has no inherent tie to JCenter or Maven Central, so you can always switch to any other repository of your choice.

And according to Android Developers:

JFrog, the company that maintains the JCenter artifact repository used by many Android projects, recently announced the deprecation and upcoming retirement of JCenter.
According to the announcement, JCenter will allow downloads of existing artifacts until February 1, 2022.

Developers who publish artifacts on JCenter should start migrating packages to a new host, such as Maven Central.

So, just make sure that the authors provide their library in other repositories and then update your build scripts to enable downloading from those repositories.
For example, in Gradle use mavenCentral() function to enable getting dependencies from Maven Central repository.

Replace jcenter() by:

gradlePluginPortal()
mavenCentral()

The latest update as mentioned here in JFrog's website is the following:

UPDATE 4/27/2021: We listened to the community and will keep JCenter as a read-only repository indefinitely. Our customers and the community can continue to rely on JCenter as a reliable mirror for Java packages.

Replace

jcenter()

with this:

mavenCentral()

In my case i have followed these steps to get it done :

1. Place mavenCentral() before jcenter()
2. Upgrade gradle using Android Studio Upgrade Assistant (in my case upgraded to 7.0.3)
3. Install NDK (Side by Side) through plugins (Android Studio)
4. Clean & Rebuild project

You have to change

jcenter()

with

mavenCentral()

moreover you have to set one or more repository urls:

repositories {
    mavenCentral()
    maven {
        url = "https://repo1.maven.org/maven2/"
    }
    maven {
        url "https://repo.spring.io/release"
    }
    maven {
        url "https://repository.jboss.org/maven2"
    }
    maven {
        url 'https://repo.jenkins-ci.org/public/'
    }
}