One of the things learnt from todays UMTS air interface is that saving power during times when no data is transmitted is of foremost importance in the day and age of always-on applications and infrequent transmission of small quantities of data. Current HSPA networks are not really refined for this yet but help is on the way with a feature pack referred to as Continuous Packet Connectivity. See here, here and here for details. With LTE, power saving mechanisms are built in from day one. One of the most important of those will be Discontinuous Reception (DRX) while in Connected State, which I'll shortly describe in this post.
The general idea of this functionality is to allow the mobile device to periodically switch off its receiver for some time before it has to listen again to the control channel to see if the network has new data for the device. On and off times can be configured dynamically down to the sub-frame level (1ms) depending on the device's activity. Switching off the transciever for some time has a negative impact on latency so a two stage approach has been implemented.
When the network configures DRX for a device it defines the value for a timer that starts running after each data block has been sent. If new data is sent the timer is restarted. If still no data was sent when the timer expires the device enteres DRX mode with an (optional) short DRX cycle. This means it will go to sleep and wake up in a short pattern. If new data comes in it can thus be delivered quite quickly because the device only sleeps for short periods. The short DRX cycle mode also has a configurable timer attached and once it expires, i.e. no data was received during the short cycle mode the device implicitly enters the long DRX cycle which is much more power efficient but further increases latency time.
Final Note: Connected Mode DRX should not be mixed up with DRX in idle mode which the mobile is set into after a prolonged time of air interface inactivity. It's also known as paging DRX, i.e. the time the mobile device can go to sleep between two paging messages which could contain a command for the mobile to wake up again and change back to Connected state. This DRX is much less fine grained and measured in hundreds of milliseconds or even seconds.