What is application of latch in VLSI design?
In many cases an increase in the throughput of a digital circuit is required, but for some reasons you cant build a pipelined version. So you end up building a pseudo-pipelined version of this circuit.
A pseudo-pipelined version of a circuit might contain latches. For example if i want to double the throughput of this digital module A

We can build the following pseudo-pipelined circuit [That include latches] to double the throughput

Every two clock cycles, one of the latchs output is changed with a new output allowing its A module to compute a valid result within this time. The new pseudo-pipelined version doubles the throughput without missing with the internal structure of A itself. So you might find latches in circuits like this