  We establish limit theorems for the maxima and minima of Airy$_1$ and
Airy$_2$ processes (denoted by $\mathcal{A}_1(\cdot)$ and
$\mathcal{A}_2(\cdot)$ respectively) over growing intervals. In particular, we
identify the finite non-zero constants that are the almost sure limits of
$(\log t)^{-2/3}\max_{0\le s \le t} \mathcal{A}_{i}(s)$ and $(\log
t)^{-1/3}\min_{0\le s \le t} \mathcal{A}_{i}(s)$ for $i=1,2$. This complements
and extends the results of (Pu, 2023), where the question for the maxima was
considered and the order of growth was identified for both $\mathcal{A}_1$ and
$\mathcal{A}_2$ and the constant was identified for $\mathcal{A}_1$. Our
approach is different from that of (Pu, 2023); instead of complicated formulae
for multi-point distributions, we rely on the well-known convergence of passage
time profiles in planar exponential last passage percolation started from
different initial conditions to $\mathcal{A}_1$ and $\mathcal{A}_2$, together
with the recently developed sharp one-point estimates in (Baslingker et al.,
2024) for the point-to-point and point-to-line passage times in exponential LPP
and a combination of old and new results on the geometry of the LPP landscape.
