This is a controversial topic and generates a lot of debates here and elsewhere. Do don't expect what follows to be definitive, but it is one answer.
'No self' or anatta
does not really mean 'there is no self' in the obvious way that it might seem. It is actually generally used as an adjective, that is, 'everything is anatta
'. And 'everything' includes the five aggregates, material form, and so on. All these are anatta
, not self, and also sunya
, empty of own-being.
But on the level of conventional truth and day to day reality, there are agents, doers of actions, who suffer or benefit from the consequences of such actions. This is so even if ultimately the doer, like everything else, is empty of own-being. Perhaps you could say, the aim of realizing no-self and emptiness is to overcome the sense of identifying with, and clinging to, all the various objects of perception - your role, identity, status, and so on - which you invest with significance because you think 'this is mine, this is me, this is what I am'. So you could see the no-self teaching as an antidote to clinging to those things, which are always transitory and don't lead to the cessation of suffering. So the sense in which such things are 'illlusory' is not that they're non-existent, it is that they don't offer the substantiality that we invest them with. They are unreal in the sense that clinging to money, power, and so on, is ultimately frustrating as they cannot bring any real satisfaction.
As I say, a difficult question, and others might have very different answers, but that is my understanding.
He that knows it, knows it not.