In Java, Reader and Writer are abstract classes that provide a way to read and write characters to a stream. They are the character-based counterparts of the byte-based InputStream and OutputStream classes.

The Reader class defines a set of methods that can be used to read character data from a stream, while the Writer class defines a set of methods that can be used to write character data to a stream.

Here are some commonly used methods of the Reader class:

1. read(): This method reads a single character from the stream and returns it as an integer.

2. read(char[] cbuf): This method reads characters into an array and returns the number of characters read.

3. read(char[] cbuf, int off, int len): This method reads characters into a portion of an array and returns the number of characters read.

4. skip(long n): This method skips over a specified number of characters in the stream.

5. mark(int readAheadLimit): This method marks the current position in the stream.

6. reset(): This method resets the stream to the previously marked position.

7. ready(): This method returns true if the stream is ready to be read.

8. close(): This method closes the stream and releases any resources associated with it.

Here are some commonly used methods of the Writer class:

1. write(int c): This method writes a single character to the stream.

2. write(char[] cbuf): This method writes an array of characters to the stream.

3. write(String str): This method writes a string to the stream.

4. write(char[] cbuf, int off, int len): This method writes a portion of an array of characters to the stream.

5. flush(): This method flushes the stream.

6. close(): This method closes the stream and releases any resources associated with it.

Both Reader and Writer classes are used extensively for processing character-based data in Java. The classes that extend from these abstract classes include FileReader, StringReader, BufferedReader, InputStreamReader, FileWriter, StringWriter, and BufferedWriter, among others.