The main advantage of VTEC and similar systems like Mitsubishi's MIVEC and Nissan's Neo VVL is that they can change both the cam timing and the valve lift resulting in maximum power at the top end. However, low-end torque does not improve much. 

This is where VVTi comes in. Unlike VTEC, VVTi does not use dual cam profiles and doesn't have a Dr.Jekyll-Mr.Hyde changeover point. Rather, it varies the intake valves' timing continuously throughout the rev range. At higher revs, it opens the valves earlier to promote better breathing. Thus the valve timing changes. However, the valve lift or how long the valves stay open, doesn't change. 

In a VVTi engine, the end of intake camshaft incorporates a gear thread. This thread is coupled with a cap that can move towards and away from the camshaft. Because the gear thread is not parallel to the axis of the camshaft, valve timing will shift forward if the cap is pushed towards the camshaft. Similarly, pulling the cap away from the camshaft results in shifting the valve timing later. Hydraulic pressure controlled by the ECU pushes or pulls the mechanism depending on engine rpm and other conditions

VVTi Engine by Toyota

The "i" denotes that the ECU adjusts valve timing not just based on engine rpm but on several factors including vehicle acceleration or deceleration, uphill or downhill direction, etc.

  
These new breed of Toyotas are the ones to use high-performance versions of the VVTi engines. 
The Mitsubishi Lancer Evo VI combines MIVEC and turbo charging to bring out 350 bhp from a 2.0-liter engine!