I am out of academia for many years, the last time I attended a conference was 15 years ago.
But I try to follow what is happening in physics and so I watched this video from the Strings 2018 conference to get an idea or at least a glimpse of the current state of string theory. (x)
One issue that got some attention was the problem to find solutions corresponding to de Sitter space (dS).
It is already difficult to formulate quantum field theory in dS, which describes an exponentially expanding universe.
In dS there is no positive conserved energy, an observer cannot witness the final state of the universe due to the horizon and therefore it is unclear how to define an S-matrix. It is believed that in dS entropy is finite and therefore it only allows for a finite number of degrees of freedom, while quantum field theory seems to have an infinite number.
And last but not least it seems that one cannot have (unbroken) susy, because there is no global timelike Killing vector.
One attempt to quantize a scalar field in dS is described in this paper.
Recently, the question has been asked "what if string theory has no de Sitter vacua?". See also Vafa et al. and Urs Schreiber's comment.
At Strings 2018, Cumrun Vafa talked about his recent paper and proposed a conjecture, which suggests a constraint on possible cosmological solutions. If we assume that this conjecture is indeed correct (*), it would follow that we live in a universe
which (currently) looks like dS, but "dark energy" would really be a manifestation of "quintessence", i.e. a slowly changing scalar field, and at some point in the future a phase transition would end it all.
(x) I really liked the Maxwell quotes.
(*)Perhaps it is worth emphasizing that at this point none of it is known for sure and, as one would expect, Peter Woit pointed that out.
added later: In his comment Urs Schreiber writes that "KKLT [..] is in the process of being abandoned for being plainly mathematically wrong". I don't think we know that.
The KKLT construction adds "antibranes" to AdS vacua to arrive at a dS solution. It has been shown in one particular case that this does not really work, but in general it is not obvious yet that it fails.
Let me be very clear that I do not really know what I am talking about - just like many string theorists.