In this talk, I will present four studies carried out for my PhD project about dynamical fluctuations in many-body systems. First, I will present a generalization of a well-known fluctuation theorem to the joint probability distribution of currents at different times, and discuss its three consequences: an extension of the Green-Kubo relation for multi-time statistics, the emergence of fractional Brownian motion in the two-time current correlation, and the full multi-time statistics for the symmetric simple exclusion process (SSEP) under equilibrium initial conditions. I will also compute the two-time correlation for the non-equilibrium SSEP. Second, I will discuss a model of population dynamics whose long-time behavior is captured by the noisy Fisher-KPP equation describing wavefront propagation between competing species. I will discuss exact solvability of the symmetric case revealing a mapping to the Lieb-Liniger model, giving access to n-point correlations. Third, I will discuss worm statistics in the close-packed dimer model on square and honeycomb lattices, finding a dynamic exponent greater than 2, indicating subdiffusive motion. Fourth, I will study the close-packed dimer model on the star lattice, which maps to square and triangular lattice Ising magnets under two fugacity sets, and characterize its equilibrium properties at criticality. All these studies reveal emergent dynamical correlations in non-equilibrium conditions.