Instability-driven fast magnetic reconnection plays a fundamental role in generating explosive dynamics and heating in solar plasmas, leading to a wide range of explosive phenomena across the solar atmosphere. However, relatively little is known about how fast reconnection develops in the lower layers of the solar atmosphere, and in particular in the chromosphere, where the plasma is partially ionised. In this Thesis, a model for partially ionised plasmas in the fluid approximation is presented to simulate magnetic reconnection events in the solar chromosphere. The partially ionised environment is modelled by the (PIP) code through a two-fluid charge-neutral hydrogen plasma (protons + electrons and neutral atoms) where charges and neutrals are coupled through elastic collisions, charge-exchange, collisional ionisation and recombination. The effects of partial ionisation on the development of plasmoid coalescence is investigated through 2.5D numerical simulations of coalescing plasmoids in a single fluid magnetohydrodynamic (MHD) model and a two-fluid model of a partially ionised plasma (PIP). Partial ionisation alters the dynamics of the coalescence instability, which promotes faster reconnection and forms a current sheet through plasmoid interaction that is subject to the onset of further instabilities and turbulent dynamics. Plasmoid coalescence is faster in PIP cases than MHD cases at the same bulk density, following the faster thinning of the current sheet and the onset of secondary plasmoid dynamics, which can form in the PIP model in linearly stable conditions and are responsible for a more violent reconnection. A second study using 2.5D simulations of coalescence instability is presented to discuss the role of collisional ionisation and recombination in accelerating reconnection. Ionisation and recombination process slow down the coalescence, stabilise current sheets and suppress non-linear dynamics, with turbulent reconnection occurring in limited cases: bursts of ionisation lead to the formation of thicker current sheets, even when radiative losses are included to cool the system. Therefore, the coalescence time scale is very sensitive to ionisation-recombination processes. Although the reconnection time scale is longer with the inclusion of ionisation and recombination, reconnection in PIP is still faster than in a fully ionised plasma environment having the same bulk density. Next, 3D simulations of partially ionised plasmas are performed to show the effects of two-fluid dynamics on the stability of flux ropes subject to the resistive kink instability in the lower regions of the solar atmosphere. Results show that partial ionisation, which result in having a smaller plasma β of the isolated plasma when compared to the total plasma β , leads to a faster onset of the non-linear phase of the kink instability. The magnetic energy lost with reconnection is distributed in a different way between MHD and PIP cases, with a larger increase of the internal energy associated to partial ionisation. The temperature of PIP cases increases faster due to further heating terms, such as the frictional heating, resulting from the two-fluid dynamics. The studies presented in this Thesis all prove that the chromospheric dynamics are in general faster and more explosive than fully ionised environments, due to the inclusion of the more complex physical processes linked to the interaction between charges and neutral elements in the plasma mixture. Violent effects and changes in the stability of features such as plasmoids are a direct consequence of partial ionisation, and not only explain the faster reconnection behind the formation of many structures observed in the chromosphere, but also lead to an exciting complex dynamics that is very interesting to investigate in detail.