The probing and understanding of quantum many-body systems poses a major challenge. Quantum simulators built from ultracold atoms emerged as a pristine platform for studying many-body systems. In QuOntM, we will use continuous many-body quantum systems to study the effective field theories describing the physics emerging on large scales. To efficiently extract physical information from those quantum simulations, it is of great importance to develop new efficient schemes for information extraction. Here, continuous observations by weak measurements promise new possibilities for information extraction and even give rise to intriguing new phenomena. Our main objective is to develop new weak quantum measurements, eventually allowing for continuous probing of many-body systems.  To verify that the emerging physics indeed fits the model that should be simulated we will develop new techniques for learning the effective Hamiltonian in continuous systems. The outcome of QuOntM will be measurement schemes acting in completely new regimes and the technological advances will directly be applicable to other experimental platforms. In future, the possibility of detecting time-time correlations will provide new fundamental insights into the dynamics of many-body quantum systems.