State of research on SHA-1 Collision Attacks
SHA-1 was SHattered by Stevens et al. They demonstrated that collisions in SHA-1 are practical. They give the first instance of a collision for SHA-1.

It is an identical-prefix collision attack that enabled the attacker to forge two distinct PDF documents that have the same SHA-1 hash value. I.e. They extended a given prefix $p$ with two distinct near-collision block pairs for any suffix $s$ that collides.

$$\operatorname{SHA-1}(p \mathbin\Vert m_0 \mathbin\Vert m_1 \mathbin\Vert s) = \operatorname{SHA-1}(p \mathbin\Vert m'_0 \mathbin\Vert m'_1 \mathbin\Vert s)$$ for any suffix $s$, where $(m_0, m_1) \neq (m'_0, m'_1)$ 

The computational requirement is estimated to $2^{63.1}$


  The first first-block near collision was found after spending about 3583 core years that had produced 180 711 partial solutions up to step 61. A second near collision block was then later computed; it required an additional 2987 core years and 148 975 partial solutions.1