To introduce yourself to the topic from the perspective of biology you might want to start by reading Ending Aging, by Aubrey de Grey. Here one of the TED Talks of the author.
In short, what changed is that starting from the early 2000s a well defined strategy to put aging under medical control (reversing it) emerged, by recognising what aging is and how medicine could target all of its facets (the "damages" or "hallmarks" of aging Aubrey de Grey and the paper linked above talk about). In more recent years this promising approach is gaining more and more momentum, in the form, for example, of human trials for senescent cells removal (senescent cells are one of the hallmarks/damages), experiments rejuvenating mice, or the foundation of several new companies. Here a map of progress that helps you watch the progression of relevant therapies in this field from early basic research to human clinical trials, and monthly and yearly roundups keeping up with what's happening.
15-20 years is probably an optimistic timeframe that assumes optimal funding and no major roadblocks, but working all together, doing advocacy and donating to research we might put aging under medical control in most people's alive today lifetimes. These short timeframe predictions rely on a concept called Longevity Escape Velocity: even if the first therapies will be imperfect they will probably buy enough time for people to be alive when the next generation of more perfected therapies will be avalable, and so on till aging is completely reversible. The evidence in favour of this is taken from the history of technology: Each subsequent improvement on an existing technology always takes far less time that the first development made by the pioneers. This happens due to the ideas behind the technology becoming accepted and understood, research becoming worldwide and funding flawing at optimal rate after the feasibility becomes evident. It's argued that that this first "proof of concept" required to convince the world is Robust Mouse Rejuvenation: doubling the remaining life expectancy of elderly mice, demonstrated and then replicated in rigorous laboratory studies. It also helps that the various facets of aging are all interacting with each other and improving one aspect should have a cascade of positive effects on the other aspects.
Regardless of the timeframe, speeding up the progress of this field is a moral imperative for many, since aging is the biggest killer on the planet, responsible for 2/3 of all deaths and countless years of suffering due to late life disability and ill health. 100000 deaths due to aging out of 150000 total deaths happen each day, amounting to more than one person per second dying because of aging.
"Immortality" in the sense of "invulnerability" or "infinite life", on the contrary, is more difficult to achieve and it may never arrive for anyone, since even after putting aging under medical control there will still be accidents and maybe infectious diseases, although probably decreasing with time given current trends. This is why in this sub we generally don't like talking in terms of "immortality", together with the fact that it tends to give off a bad impression when trying to educate people on the topic. It's not very scientific as a term, it's too much linked to fiction, and it belongs more to bad science popularisations.
I don't think you're asking the right researchers the right questions. Aubrey de Grey lays out his SENS strategy in Ending Aging the 8 or 9 different problems that need to be solved - cross-linking of proteins, mitochondria mutation, accumulation of senescent cells etc.