The basic forms are in the following table:
|To-infinitive (simple)||there to be|
|To-infinitive (perfect)||there to have been|
|Bare infinitive (simple)||there be|
|Bare infinitive (perfect)||there have been|
|Gerund (simple)||there being|
|Gerund (perfect)||there having been|
|Present simple||there is||there are|
|Present perfect||there has been||there have been|
|Past simple||there was||there were|
|Past perfect||there had been|
Note that while the perfect aspect can apply, the progressive aspect can't be applied; we don't say *"there are being".
With modal verbs
In addition, "there be" can take modal verbs, both full modal verbs and semi-modal verbs. Note that in these constructions, there is no object agreement, as they all take an infinitive; either a bare infinitive or to-infinitive.
|can||there can be||?there can have been|
|could||there could be||there could have been|
|will||there will be||there will have been|
|would||there would be||there would have been|
|May||there may be||there may have been|
|might||there might be||there might have been|
|shall||there shall be||there shall have been|
|should||there should be||there should have been|
|must||there must be||there must have been|
|ought to||there ought to be||there ought to have been|
|need to||there needs to be||there needs to have been|
|have to||there have to be||there have/has to have been|
|used to||there used to be||-|
For those with non-rhotic pronunciation, a linking /r/ is often desirable in "there are", especially to distinguish it from "they are", which has a linking /j/. There's little point students thinking of the right grammar, and then saying something that sounds like e.g. *"they are two pens on the table".
Are in there are is often reduced to a schwa - /ðeərə/. There were is similarly reduced to /ðeəwə/, and there was to /ðeəwəz/, etc, etc. [table needed]
Chinese students will often try to say *"there has", or *"there have", or just *"have" or *"has" (without a subject). This is because in similar situations in Chinese, they use 有 (Pinyin: yòu). This frequently develops into a fossilised error.