Because of the very nature of subatomic objects, it is impossible, even in theory, to know with arbitrary precision both the position and velocity of any given wave / particle; position and velocity can only be described in terms of probabilities.
It cannot be overstated that this limitation is not caused by any technological or theoretical failure; it is simply the nature of the quantum world to be indeterminate. Suppose we try to pin down the exact location of an electron through a microscope. If we have to 'see' the electron, it means the electron should scatter the light into our eyes, or some other light-detector. But we learnt that if the electron absorbs a photon, it gains energy and is disturbed. It induces an uncertainty in the particle's velocity. On the other hand, if we try to use a low-energy beam of light, we cannot determine the position of the electron with surety.
Thus the fundamental laws of nature conspire to keep the objective reality of the atomic and sub-atomic world veiled from us. For example, electrons around an atomic nucleus appear to be in a hazy cloud. The sharp paths or orbits remain forever hidden from us.
This principle applies equally to any object, but its effect is negligible for an object of everyday size. In fact, ordinary experimental uncertainties harm the observation much more than Heisenberg's principle! This is the reason why Newtonian classical physics was so successful in explaining real-world phenomena.
Any observation disturbs a system under study; in non-quantum systems one can reduce the disturbance arbitrarily. In any case, one can compute, at least in principle, effects of the disturbance dictated by deterministic laws and subtract them out. This is impossible in the quantum domain even in principle.
Many physicists working at the time of the quantum revolution found this fact very difficult to accept. One notable figure was Albert Einstein himself, who refused even to his dying day that any part of the universe could be indeterminate by nature. Part of the reason for this difficulty is that most of the physicists of that time had been trained in classical mechanics, which very much shaped their thinking. The other part of the difficulty is that it is impossible for the human mind to imagine something that is actually indeterminate. In the world of human experience, we only find determinate things. For example, you will never find a cat which is neither alive nor dead, but in an in-between indeterminate state. All cats are either alive or dead; indeed, all macroscopic objects have a determinate state which can be observed and described (at least in theory). This is in no way true of the quantum world which had been discovered.
In time physicists learnt to accept the fact of indeterminacy, even though they could not imagine it. The ones who could not accept it eventually died. At the beginning of the twenty-first century, there are virtually no physicists who reject quantum physics. There is certainly disagreement about the meaning of quantum physics, but that is really more a matter of philosophy.
Once physicists realised that quantum hypothesis is not compatible with determinism -- this was the breakthrough -- they tried to find answers to the objections raised in Bohr's model differently. The next chapter explains how.