In the motivational part, we explore a possibility that the fundamental Theory of Everything is not a variant of string theory, but some version of conventional field theory defined in flat higher-dimensional bulk. Our curved Universe may represent a kind of 3-brane solution in this theory. To be renormalizable, this theory should involve higher derivatives in the Lagrangian. In such systems, the spectrum of the quantum Hamiltonian does not have a ground state - the levels with arbitrary negative energies exist. This phenomenon (the ghosts) is usually considered as a serious pathology leading to paradoxes and inconsistencies. We point out, however, that, by themselves, ghosts do not represent a major problem. There is no problem whatsoever for free theories. The danger consists in quantum collapse where the system runs into a singularity. The probability “leaks” into the singularity, and unitarity is violated. This behavior is characteristic, indeed, for the most ghost-ridden theories. But this does not always happen. We present certain quantum mechanical and field theory models with “benign” ghosts where the collapse does not happen, the Hamiltonian is kept Hermitian and a unitary evolution operator can be defined.