The object of meditation I have been focused on the breath in meditation and I am interested in Vipassana, but I am confused about the object of meditation.

I have read that you focus on the breath and as thoughts arise, you should observe them and then return to the breath and that it is the returning to the breath that increases one's mindfulness.  I have also read that in Vipassana meditation, one shifts the object of meditation to the thoughts that arise and make them the object of mediation.

This approach seems to be just sitting and letting your thoughts wander.  Do I misunderstand the meaning of making arising thoughts the object of meditation?  As it is now, I continue to make the breath the object and observe my other thoughts but generally do not pursue them, rather just categorizing the thought (like "planning the future" or "reliving the past") and then return to the breath.
In the meditation taught in the original Buddhist scriptures, the mind stays with the breath &amp; free from thought.

In the original Buddhist scriptures, there is no 'shift' when vipassana is practised. Instead, calmness (samatha) &amp; insight (vipassana) are developed simultaneously. The scriptures state: 


  These two qualities occur in tandem: tranquillity &amp; insight.
  
  MN 149


In the original Buddhist scriptures, the term 'vipassana' refers to the 'clear seeing' of the impermanent (anicca), unsatisfactory (dukkha) &amp; not-self (anatta) characteristics of the five aggregates (body/breathing; feeling sensation; perception; thought/mood; sense consciousness). 

For example, the breath arises &amp; passes continually; a breath appears &amp; disappears; a new breath appears, then disappears; another breath appears then disappears. To see/experience clearly impermanence of breathing is vipassana. 

To see clearly that it is the physical body that breathes (rather than the 'self' or 'I' that breathes) is also vipassana of 'not-self' in relation to breathing. 

'Unsatisfactoriness' means to see that because X breath &amp; Y breath is impermanent; that breath cannot form the basis of or be relied on for lasting happiness (due to its fleeting impermanent nature). It can also mean the impermanent nature of a breath, if clung to, will lead to suffering. 

The ordinary distracting thoughts the mind has are not really suitable for vipassana because they actually diminish awareness, clarity &amp; discernment of the mind. 

For the mind to practise effective 'vipassana' in relation to thought (sankhara aggregate), 'samadhi' (mental clarity &amp; stability, aka 'concentration') must ideally be very developed &amp; pure (empty). 

Ultimately, true 'vipassana' is 'enlightenment'. It is very profound because it discerns the 'not-self' nature of the five aggregates.

Believing 'you' are observing 'your thoughts' or thinking 'my thoughts' are impermanent is not really vipassana because vipassana sees 'not-mine' or 'not-yours' (anatta) rather than 'my' or 'yours'. 

To conclude, categorizing the thought (like "planning the future" or "reliving the past") and then return to the breath is the right method according to the original scriptures.


  You shouldn't chase after the past or place expectations on the future. What is past     is left behind. The future  is as yet unreached.
  Whatever phenomena/truth (dhamma) is present you clearly see right there,
       right there. Not taken in, unshaken, that's how you develop the heart.
  
  Bhaddekaratta Sutta