The popular account of Milgram's work is that 'people obey orders no matter how extreme'. That is based on just one study - the so-called 'revised baseline condition' in which 65% continued shocking to the end.
But Milgram didn't do just one study. He ran some 30 variants...

And in those variants, obedience varied from 0% to 100%. So to ask 'would people still obey today' misses the point that people didn't always obey back then - it depended critically on the condition.

So the important question is how these conditions affect obedience and why. That is, what are the key processes which affect whether we obey or not - in 2020 as in 1960. And this is where even Milgram's greatest fans acknowledge that his account is inadequate.

That is, Milgram rrervealed a disturbing phenomenon but didn't explain it. Recent research has tried to fill that gap. Our own account is in terms of 'engaged followership'. This focusses on the active leadership of the experimenter and the active choice of the participant.

So, the experimenter tries to persuade the participant that they are part of a team promoting a worthwhile cause (understanding how people learn) and that by engaging with it they are furthering a grreater good.

The participant, who knows full well how the victim is suffering, continues with the shocks to the extent that they identify with the experimenter and with the scientific cause. They don't find this easy but they feel that they (like the victim) are suffering for a cause.

In sum, people inflict harm, not because they are unaware of what they are doing but because they believe that they are doing good. And this doesn't happen spontaneously. It is critically dependent on toxic leadership... a message of great relevance today.

If you want to follow this up, and reading some of our publication on this issue, you can find them here: http://www.bbcprisonstudy.org/resources.php?p=138
You might also be intertested in this paper which applies the same analysis to Zimbardo's Stanford Prison Experiment: https://psycnet.apa.org/record/2019-45342-001