one of the most well known questions of erdos in discrete geometry is the following: given n points in $r^d$, what is the smallest number of distinct distances among them ? here d is fixed and n tends to inifnity. we denote by $f_d(n)$ is smallest number of distince distances. the problem of determining $f_d(n)$ has been attacked by many researchers (including erdos, beck, chung, trotter, szemeredi, beck, ssekely, solymosi-toth, sharir, etc) for decades. in this talk, i will give a brief overview and also present a new result (joint with solymosi). this result gives an almost sharp estimate for $f_d(n)$ for relatively large dimension $d$. the main tool is what we call "decomposition technique", which appears to be useful in other problems as well.