The prime number theorem in short intervals states $\psi(x+h) - \psi(x) \sim h$, where $h = o(x)$ and $\psi(x)$ is the Chebyshev $\psi$-function. This is known to be true as long as $h$ is not too small. Furthermore, it is a natural extension of the prime number theorem. Using a new smoothing approach and assuming the Riemann Hypothesis, I will describe how to establish the strongest explicit description of the error in $\psi(x+h) - \psi(x) \sim h$, when $\sqrt{x}\log{x} \leq h \leq x^{3/4}$. Further, I will also present future avenues of research related to this result.