Smoothish points in-between known points in a time series

Question

I have a bad feeling this is a well explored field I should already know about, but

Say you have some platonic data at given points

...
at 13.0:   1000
at 14.0:   1152
at 15.0:   1000
at 16.0:   1200
...

(of course, the times needn't be regular, but let's carry on)

For any abstract point, you could use the naive strategy of "nearest" point

equally pathetically, make a line between the two around you

What's the technique if you want a smoothish line?

(Obviously, you could adopt different smoothing strategies for different smoothing concepts, but, some solution.)

What's the algorithm in a sense of "let's make some computer code" for this? I'm guessing it's along the lines of weighting with some diminishing number of points around you, but this has surely all been well-considered.

Secondly, is what I am describing here "smoothing a time series" or am I totally offbase?

Thirdly does this have anything to do with RMS or am I offbase?