The hypothesis is usually stated in three forms that differ in how much information they claim prices already reflect. The weak form says prices reflect all past price and volume data, so technical analysis (the study of past price patterns) cannot reliably generate excess returns. The semi-strong form says prices reflect all publicly available information, including financial statements and news, so fundamental analysis of public data cannot reliably win either, because everyone else has the same data. The strong form says prices reflect all information, public and private, so even insider information could not beat the market; this form is the least defensible and is largely contradicted by the fact that insider trading is both illegal and profitable when it occurs. Most evidence is consistent with markets being somewhere around weak-to-semi-strong efficient: hard to beat with public information, not perfectly efficient.
A crucial and often-missed point is that the hypothesis is joint with whatever model of "fair" return is used to test it. To say a return was abnormal, one must first say what a normal return should have been, and that requires a risk model. So a finding that some strategy "beat the market" can mean the market was inefficient, or it can mean the risk model was incomplete and the strategy was simply being paid for a risk the model did not measure. Much of what once looked like evidence against efficiency turned out, on closer inspection, to be compensation for identifiable risk factors rather than free money, which is where the study of factor investing grew from.
The hypothesis has serious challengers, and honesty requires naming them. Behavioral finance documents that investors are systematically prone to errors (overreaction, herding, loss aversion) and argues that these can push prices away from fundamental value for extended periods, with asset bubbles as the dramatic case. The efficient-market response is that exploiting even a real mispricing is dangerous and costly (prices can stay wrong longer than a contrarian can stay solvent), so the difficulty of beating the market can survive even if prices are not always right. The debate is genuinely unresolved among credible economists. What is not seriously disputed is the practical takeaway that most active managers, after fees, fail to beat the market over long periods, which is the part of the hypothesis with the strongest evidence behind it.