  To capture the extremal behaviour of complex environmental phenomena in
practice, flexi\-ble techniques for modelling tail behaviour are required. In
this paper, we introduce a variety of such methods, which were used by the
Lancopula Utopiversity team to tackle the EVA (2023) Conference Data Challenge.
This data challenge was split into four challenges, labelled C1-C4. Challenges
C1 and C2 comprise univariate problems, where the goal is to estimate extreme
quantiles for a non-stationary time series exhibiting several complex features.
For these, we propose a flexible modelling technique, based on generalised
additive models, with diagnostics indicating generally good performance for the
observed data. Challenges C3 and C4 concern multivariate problems where the
focus is on estimating joint extremal probabilities. For challenge C3, we
propose an extension of available models in the multivariate literature and use
this framework to estimate extreme probabilities in the presence of
non-stationary dependence. Finally, for challenge C4, which concerns a 50
dimensional random vector, we employ a clustering technique to achieve
dimension reduction and use a conditional modelling approach to estimate
extremal probabilities across independent groups of variables.
