Which of real time, real-time and realtime is correct when you are talking about seeing something as it happens?
The difference between "real time" and "real-time" is mostly a matter of style and placement. In most cases, there's no need to add the hyphen; "real time" will work very well. However, a case can be made for its use where it would clarify the writing. For example:
I am updating this in real time.
This is a real-time update.
In the second sentence, there's no real need to have the hyphen. However, a reader could stumble a bit on the "real", not realizing that the adjective is "real time". However, this is an extremely minor point, and is rarely done in practice. (In this case, it'd be carrying clarity almost to the point of silliness.)
A better use of the hyphenated form would be "real-time signal processing", so it's not confused with processing that's both real and the processing of time signals. Oxford points out this usage. If you're using this term in a computing sense and the domain you are working in has no precedent to offer, I'd use the hyphen when in doubt.
As to "realtime":
As words are commonly paired together, they tend to be spelled as one word...eventually. "Realtime" isn't a word in any dictionary I can find, but it does get used in slang and in names. American dictionaries tend to list these combination words before UK dictionaries.
In other words, we'll see "realtime" in more dictionaries. It's just a matter of time. (Really.)
All three are correct. Wikipedia, defining "real-time"/"realtime"/"real time":
Real-time, real time, or realtime may refer to:
Real time (media), a narrative technique in which the events depicted take place entirely within the span of the depiction, and at the same rate
Real-time computing, the study of computer systems which are subject to a real-time constraint
This doesn't mean that "real time" is used for media, or "real-time" for computing, as in the link provided, other examples show that all of these terms are interchangeable.
What the above quote does show is that "real time" or "realtime" is used as a noun (and can also be used as an adjective), but "real-time" is used as an adjective only.
As an example:
Real time: a synonym for presentism in philosophy of time
Real-time: a synonym for the present, as events happen
Note, how "real time" is a noun, whereas "real-time" is an adjective.
Looking at the Google Ngrams Viewer:
Interesting to note that "real-time" doesn't seem to appear much in books, but perhaps the reason is because it was coined to describe computing, and hence may be used a lot on the internet, but not in books.
For realtime, I've always followed Rule #4 in the Grammar book. http://www.grammarbook.com/punctuation/hyphens.asp
Notice that I used it as one word in my last sentence. In that case, I did so because it was a noun and not a compound adjective.
As a writer, I believe it's often more important to be consistent than correct. If I have clients who insist on using it one way or the other, I just go with the flow.