Abstract: In this paper, we will associated with our works to state some new advance in the theory of strong approximations.There are five parts in the paper, i.e.1.Increments of a Wiener process.2.Strong approximations for partial sums of IIDRV’s.3.The increments of partial sums of independent R.V.s （non-identically distri- buted）.4.Strong approximations of mixing R V.s.5.Strong approximations for other kinds of dependent R.V.’s and functional of R.V.s.