How can I upgrade to Java 1.8 on an Amazon Linux Server?

I tried sudo yum update but it just keeps java "1.7.0_75". I need 1.8 for it to work with another application but can't figure out how to upgrade it.
Do I need to manually install it somehow? There's not much information on this on the internet as far as I can see.
Specs:

java version "1.7.0_75"
OpenJDK Runtime Environment (amzn-2.5.4.0.53.amzn1-x86_64 u75-b13)
OpenJDK 64-Bit Server VM (build 24.75-b04, mixed mode)

When I try update now:

[ec2-________]$ sudo yum update
Loaded plugins: priorities, update-motd, upgrade-helper
amzn-main/latest                                         | 2.1 kB     00:00
amzn-updates/latest                                      | 2.3 kB     00:00
No packages marked for update

Is there anything else I need to do?
Thanks.

To remove java 1.7 and install java 1.8:

sudo yum install java-1.8.0
sudo yum remove java-1.7.0-openjdk

Install Java Runtime 1.8

sudo yum install java-1.8.0

or if you need a java compiler and other developer tools:

sudo yum install java-1.8.0-openjdk-devel

Then use the alternatives command to make Java 1.8 the default.

sudo /usr/sbin/alternatives --config java
sudo /usr/sbin/alternatives --config javac
# etc

If you prefer you can remove Java 1.7 with

sudo yum remove java-1.7.0-openjdk

but remove it after you installed Java 1.8 or the aws-apitools will also be removed as they depend on Java on being installed.

yum install java-1.8.0 -y
/usr/sbin/alternatives --set java /usr/lib/jvm/jre-1.8.0-openjdk.x86_64/bin/java
/usr/sbin/alternatives --set javac /usr/lib/jvm/jre-1.8.0-openjdk.x86_64/bin/javac
yum remove java-1.7.0-openjdk