Abstract: If $k$ is a number field, $G_k=\mathrm{Gal}(\overline{k}|k)$ its absolute Galois group and $p$ a prime number, $p$-adic Galois representations $\rho: G_k\to GL_n(\mathbb{Q}_p)$ naturally arise in algebraic geometry, coming from the action of $G_k$ on etale cohomology groups of varieties defined over $k$. Fontaine and Mazur make a fundamental conjecture giving a precise characterization of those $p$-adic representations 'coming from algebraic geometry' in the above sense. In this talk we discuss consequences of the Fontaine-Mazur Conjecture for representations which are unramified at primes above $p$. After recalling results due to N. Boston and K. Wingberg providing evidence for the conjecture in the unramified case, we report on recent work on tamely ramified pro-$p$-extensions of $\mathbb{Q}$ by J. Labute.