This order, although it was specifically directed to Prophet Muhammad S.A.W (PBUH), most Islamic scholars agreed that it should also be applicable (although not compulsory) to all Muslims since Prophet Muhammad S.A.W. (PBUH) is the perfect example and guide for all Muslims in all matters.
Moreover, performing Tahajuud prayers regularly qualifies a person as one of the righteous and helps one earn Allah's bounty and mercy. In praising those who perform the late night prayer, Allah says
When to perform Tahajjud prayer? Tahajjud may be performed in the early part of the night, the middle part of the night or the later part of the night, but after the obligatory Isha' prayer (night prayer). Commenting on this subject, Ibn Hajar says, " There is no specific time in which the Prophet (PBUH) would perform his late night prayer but he used to do whatever was easiest for him. 'Amr ibn 'Absah claimed that he heard the Prophet (PBUH) says, "The closest that a servant comes to his Lord is during the middle of the latter portion of the night. If we can be among those who remember Allah the Exalted One at that time, then do so". -At-Tirmidhi.
Now, let's view at what Allah explains about Tahajjud prayer in surah Al-Muzzaqmil (73) :-
Al-Muzzammil (73:1 to 3)