Edmund Gettier's 1963 paper "Is Justified True Belief Knowledge?" is among the most consequential short pieces in the history of philosophy. In barely three pages, he presented two counterexamples showing that a belief can be justified, true, and still fail to be knowledge, because the justification connects to the truth only by accident.
Here is the canonical version of a Gettier case. Smith and Jones are both interviewing for a job. Smith has strong evidence, the hiring manager told him directly, that Jones will get the job. Smith also happens to know that Jones has ten coins in his pocket (he counted them himself). Smith forms the justified belief: "The man who will get the job has ten coins in his pocket." As it turns out, Smith himself gets the job, not Jones. But Smith also happens to have ten coins in his own pocket, though he didn't know this. So Smith's belief is true (the man who got the job does have ten coins), justified (he had excellent evidence), but it is clearly not knowledge, the truth of the belief has nothing to do with Smith's evidence. The evidence was about Jones; the truth is about Smith.
What Gettier demonstrates is that justification and truth can come apart in a way that creates a structural gap. The belief is true, the justification is solid, but they are not connected to each other in the right way. The truth is reached through a kind of epistemic luck, the justified belief was pointing in the wrong direction, and happened to land on a truth by coincidence.
Each Gettier case contains a belief which is true and well justified without, according to epistemologists as a whole, being knowledge.
— Internet Encyclopedia of Philosophy, 'Gettier Problems'
The fallout was enormous. Philosophers spent decades proposing additional conditions to patch the JTB account. The no-false-lemma approach required that the justification not pass through any false intermediate step, but counterexamples showed this was too strong. The causal theory (Alvin Goldman's early work) required that the truth of the belief be causally connected to the belief, but this too generated its own counterexamples. The safety condition required that the belief could not easily have been false, but edge cases proliferated.
The deeper issue Gettier exposed is a tension between two dimensions of knowledge that JTB had run together: epistemic appropriateness (is the belief well-grounded from the believer's perspective?) and ontological correctness (is the belief actually tracking the right feature of reality?). A belief can score perfectly on the first and still fail the second if the world cooperates coincidentally rather than because of the believer's methods.
This tension drove epistemology toward externalism, the view that what makes a belief knowledge is partly a matter of factors external to the believer's psychological perspective. The most influential externalist theory is process reliabilism, developed by Alvin Goldman: a belief counts as justified knowledge if it is produced by a reliable belief-forming process, one that tends to produce true beliefs. You don't need to know that your perceptual faculties are reliable; it is enough that they actually are. Children and animals can have justified beliefs this way, without any sophisticated self-reflection about their epistemic situation.
Reliabilism solves the Gettier problem neatly: in Smith's case, the belief-forming process (reasoning about Jones) was not reliably connected to the truth about who got the job. The process was locally reliable, it would have worked if Jones had gotten the job, but globally unlucky. The knowledge condition requires the process to be actually truth-conducive, not just apparently so.
But reliabilism generates its own hard cases. The new evil demon problem asks: suppose two people are intrinsically identical, same experiences, same reasoning, but one is in the real world and one is deceived by an evil demon. The demon-victim's belief-forming processes are globally unreliable (all their perceptions are false), yet intuitively they seem equally justified as their real-world counterpart. Reliabilism says the demon-victim has no justified beliefs; internalists say this is absurd.
Quick reflection
Reliabilism says the demon-victim's beliefs are not justified because the process is unreliable. The internalist says they are just as justified as the real-world twin. Which verdict feels right to you — and what does your answer reveal about what you think justification is for?