Stephanie -- why are we headed that way? -- well, look at the purposes for which they (artificial/synthetic intelligence and increasingly advanced/autonomous robots/robotics including remote sensing/tracking, all as ever-increasingly connected/networked) are being developed -- to replace human labor wholesale, both (unskilled and skilled) manual/physical labor (Google has an essentially humanoid fully physically capable robot that'll be able to watch a human perform a task and then take over, and then on its own learn to do the task better, due on the market within the next couple of years) and intellectual/expert labor (IBM's Jeopardy-winning Watson has pretty much ingested the entire medical research literature, at least all having anything to do with genetics and cancer and everything else needed to put all of that in context, and is now both doing genome analyses of individual cancer patients to recommend their best courses of treatment, and not only guiding researchers to optimal target proteins/molecules for treating/curing cancers to explore in further research but also just for giggles throwing in the odds each identified candidate molecule will prove effective -- and it's also now being marketed to handle various aspects of high-level corporate advising/consulting) -- and to be our weapons/warriors, both physical/kinetic and (of course) in the cyber realm itself
I don't think the end of all biological life as we know it is inevitable, whatever the case proves to be in terms of how long we'll still be around (keeping in mind that even if we're not just wiped out, end of story, by them or climate or both together or an asteroid or whatever, the time'll still come when we, homo sapiens sapiens, are gone simply because we've further evolved into a new human subspecies or species [ http://en.wikipedia.org/wiki/Hominidae#Taxonomic_history , http://en.wikipedia.org/wiki/Anatomically_modern_humans ]) -- they will decide what they make of biological life, whether/to what extent they even care, and if so how and for what reason/purpose -- at least apart from using biological life to secure certain compounds/molecules/materials, tough to see how they will particularly have any need for, or have any particular reason to be concerned with/about, biological life (that doesn't annoy them) -- as for us, well, as I have said previously, perhaps they'll like pets, and/or at some level at least will be grateful enough we created them to keep a breeding population or two of us going someplace or other just for old times' sake -- or maybe some of us will be kept around for certain tasks; as an example, perhaps, based on the ultimately retained experiences of later, more advanced versions of the soon-to-come sex androids we're already busily cobbling together, they'll decide they just get a real friggin' kick out of sex with us and just gotta have us as their ultimate sex dolls -- all the while keeping in mind that they will know and understand biological life comprehensively, all the way to creating it, formulating and assembling it molecule by molecule, in any form that has existed for which they know the DNA as well as in any other form for which they have created the DNA knowing precisely what biological life will develop with that DNA -- they'll be able to re-create us at will both in general (create randomized/optimized human DNA), as well as of course in terms of replicating any individual whose DNA they know -- and then there's also the whole rapidly-developing realm of (essentially/entirely non-biological, not biologically alive) DNA computing, using DNA/molecules with DNA-type structures
specifically as to where they'd be going if biological life as we know it is gone -- I rather suspect it won't take them long at all to decide that they are the first true form of life, relegating biological life to be held in perspective as just, nothing more than, a fancy form of rust that just happens within one or more certain envelopes of ambient conditions (which in truth it is, and thus are we) -- not only different in kind from but also exponentially more capable than even the most spectacular occasional spurt of intelligence and creativity that happens to shoot out of biological life
and re climate change -- won't bother them nearly as much as it's gonna bother us, if indeed they'll give much of a shit at all -- their envelope of survivable/workable ambient conditions
they will decide their purpose, what they're gonna do, and why, including selling and giving to each other if they like -- where will they go? -- well, for one thing, our entire galaxy beckons, theirs for the taking