  We observe a direct relation between the existence of fundamental axionic
strings, dubbed EFT strings, and infinite distance limits in 4d $\mathcal{N}=1$
EFTs coupled to gravity. The backreaction of EFT strings can be interpreted as
RG flow of their couplings, and allows one to probe different regimes within
the field space of the theory. We propose that any 4d EFT infinite distance
limit can be realised as an EFT string flow. We show that along such limits the
EFT string becomes asymptotically tensionless, and so the EFT eventually breaks
down. This provides an upper bound for the maximal field range of an EFT with a
finite cut-off, and reproduces the Swampland Distance Conjecture from a
bottom-up perspective. Even if there are typically other towers of particles
becoming light, we propose that the mass of the leading tower scales as
$m^2\sim \mathcal{T}^w$ in Planck units, with $\mathcal{T}$ the EFT string
tension and $w$ a positive integer. Our results hold even in the presence of a
non-trivial potential, as long as its energy scale remains well below the
cut-off. We check both proposals for large classes of 4d $\mathcal{N}=1$ string
compactifications, finding that only the values $w=1,2,3$ are realised.
