As of Jellybean (4.1) you need the following permission: <uses-permission android:name="android.permission.READ_CALL_LOG" />
Code:
Uri allCalls = Uri.parse("content://call_log/calls");
Cursor c = managedQuery(allCalls, null, null, null, null);
String num= c.getString(c.getColumnIndex(CallLog.Calls.NUMBER));// for number
String name= c.getString(c.getColumnIndex(CallLog.Calls.CACHED_NAME));// for name
String duration = c.getString(c.getColumnIndex(CallLog.Calls.DURATION));// for duration
int type = Integer.parseInt(c.getString(c.getColumnIndex(CallLog.Calls.TYPE)));// for call type, Incoming or out going.
Those permissions are very sensitive and you will have to prove that your application needs them. But even if it really needs them Google Play Support team may easily reject your request without proper explanations.
This is what happened to me. After providing all the needed information along with the Demonstration video of my application it was rejected with the explanation that my "account is not authorized to provide a certain use case solution in my application" (the list of use cases they may consider as an exception is listed on that Policy page). No link to any policy statement was provided to explain what it all means. Basically they just judged my app as not to go without proper explanation.
I wish you good luck of cause with your applications guys but be careful.