I find the absence of mental disturbance that sometimes happens during meditation to be a pleasant experience. Sometimes I can induce it by visualising the spaciousness of open moorland or the vast interior of a medieval cathedral, for example. A useful insight arising from such deep concentration is the conditionality of the tranquillity…
“Everything that happens in the mind can be thought of as existing ‘somewhere,’ as if in a mental space. You turn your attention away from the characteristics of whatever is in the mind and towards the ‘space’ it occupies. This infinite space is your object of contemplation.”
– Bhante Henepola Gunaratana on attaining The Sphere of Infinite Space 
In order to aid theoretical understanding it is customary to speak of vipassana or ‘insight meditation’ and samatha or ‘concentration meditation’, but to think them two separate paths to enlightenment would be a misunderstanding. In fact, the two are really one – they are the method that Buddha gave us to attain liberation from dukkha or mental disturbance. The mind is first made tranquil by one-pointed concentration (usually on the breath); with laser-like precision, the spotlight of attention is then focussed purposefully upon the mind’s spaciousness or upon whatever arises within it. Keep doing this long enough and insight naturally follows…
Traditionally, the realms of the mind are described as an eightfold series of increasingly subtle states or jhanas: numbers one to four are the rupa jhanas and attained by concentrating on form or materiality (usually the breath), numbers five to eight are the arupa jhanas and attained by concentrating on formlessness or non-materiality (i.e. the medium or ‘space’ in which thoughts and physical sensations arise). Commentaries on jhana meditation may give one the impression that it is like riding an elevator: as concentration deepens, one progresses blissfully upwards through each of the material realms and each of the non-material realms until the state of ‘neither perception nor non-perception’ is reached – an experience very different from being lost in thoughts or feeling sleepy.
Again, the descriptions of the Jhanas are useful as an intellectual understanding tool but I personally find them less helpful as marker posts for assessing my own level of Jhana attainment. It doesn’t really matter to me which Jhana I’m in or not in – what matters is whether I’m alert or not to the presence/absence of mental disturbance and energetic/patient enough to stick at observing it. 
I find the absence of mental disturbance that sometimes happens during meditation to be a pleasant experience. Sometimes I can induce it by visualising the spaciousness of open moorland or the vast interior of a medieval cathedral, for example. A useful insight arising from such deep concentration is the conditionality of the tranquillity; being dependent upon a particular technique it is impermanent, not the bliss of nibbana, and so not worth getting excited about!
 Bhante Henepola Gunaratana, Beyond Mindfulness in Plain English, Boston: Wisdom Publications, 2009, pp. 107-8.
 “An ideal state of concentration for giving rise to insight is one that you can analyze in terms of stress and the absence of stress even while you’re in it.” Thanissaro Bhikkhu, ‘Jhana Not by the Numbers’, Access to Insight, 2011.
Access to Insight (Ed), ‘Jhana: jhana’, Access to Insight, 2005.
Access to Insight (Ed), ‘Right Concentration: samma samadhi’, Access to Insight, 2005.
Ajaan Lee Dhammadharo (Tr Thanissaro Bhikkhu), ‘The Path to Peace and Freedom for the Mind’, Access to Insight, 1995, sections VII. ‘Right Mindfulness’ and VIII. ‘Right Concentration’.
Bhante Henepola Gunaratana, ‘The Jhanas in Theravada Buddhist Meditation’, Access to Insight, 1995.