Prime geodesic theorem over $\mathbb{Z}$ and $\mathbb{Z}[i]$

I will give an overview of the status of the prime geodesic theorem over $\mathbb{Z}$ and $\mathbb{Z}[i]$. In the last few years this topic has been an active area of research in analytic number theory and I will describe the most recent results. The proofs rely mainly on the spectral theory of automorphic forms, but have connections to L-functions, class numbers and Kloosterman sums.