I will give a (biased) review on the main current ideas to explain the fundamental nature of Dark Energy using string theory. The possibility of a de Sitter vacuum in string theory, corresponding to a cosmological constant with w=-1, has proven difficult to achieve, leading to the conjecture that such vacua might lie in the String Theory Swampland. Other interesting string candidates include axion or runaway quintessence. I will in particular discuss the Thermal Dark Energy proposal. Here finite temperature effects in a light hidden sector hold a hidden scalar away from the minimum of its zero-temperature potential, leading to an effective cosmological constant, consistently with the Swampland Conjectures and with potentially observable consequences. [please email a.held@imperial.ac.uk for zoom link or password]

An early epoch of cosmic inflation, driven by a scalar field slowly rolling down a flat potential, provides an elegant solution to several cosmological puzzles. The notorious sensitivity of the slow roll potential to quantum gravity effects, presents both a challenge and opportunity for string theory to connect to observations. A very promising way to explain slow roll inflation is with an axionic inflaton field, whose flat potential is protected by a perturbative shift symmetry. However, the canonical models of axion inflation - "Natural Inflation" and "Axion Monodromy" - are now both in tension with observations and difficult to embed in a UV complete theory like string theory. I will discuss these challenges, and also a way to overcome them, with an inflationary mechanism - beyond slow roll - that is well-motivated from string theory and consistent with observations, including distinctive signatures to be searched for in future observations.