Zend_Lucene is an implementation of the Lucene search engine in PHP5 and is included as part of the Zend Framework from version 1.6. Lucene implements all of the standard search engine query syntaxes (eg. boolean and wildcard searches) and stores its index as files so it doesn't need a database server to run. Lucene can be used if you want to add search functionality to a site but don't want to go down the route of building a querying syntax from scratch.
The Zend_Cache class is part of the Zend Framework and is used (as its name suggests) to cache things. This can be anything from the front end browser output to the outcome of a complex calculation or even the results of database queries. Zend_Cache is an enormous topic, not just how the class works, but what the best practices are for caching.
I had a situation the other day where I had an application in Zend Framework and I wanted to redirect a user to another page. This is fine if you are inside a controller as you can use the _redirect() controller helper, but in this instance I was running the code from inside a plugin and so therefore didn't have direct access to the controller.
After setting up your session management in your application using one of the Zend_Auth adapters you might want to allow users to stay logged in. What you need to do is set some configuration options in the Zend_Session object. Zend_Auth uses Zend_Session as an object orientated way of manipulating the $_SESSION variable. Any changes you make to the Zend_Session object will affect the Zend_Auth object, as long as you set these options before the sessions are started.
One useful function of any application is to report on any errors that occurred. Zend Framework comes with a nice error controller system that you can activate by creating an ErrorController class.
The following is an ErrorController class that I use. It detects what sort of error occurred and displays a message to the user. It will also email a detailed report of the error to the server admins.
Zend Framework is a PHP framework, written and maintained by Zend. It is designed to make development of web applications secure, streamlined and reliable.
As with all frameworks there is a learning curve with Zend. However, as soon as you get over this it gets a lot easier. I found that the best way to understand how to program with the Zend Framework is to find some tutorials. Luckily, there are people out there who have created a few Zend tutorials.