Companies will often look to sponsor influential blogs within their niche. This usually includes having the brand mentioned within the header/sidebar of your website or even having cross-branding across the whole blog.
Advantages: If you have a relatively old domain or a lot of good quality links pointing to your website, a lot of companies would be interested in sponsoring your site with the proviso of getting a few backlinks from you.
This is a fairly common link building strategy that's used by companies to boost their search engine rankings, so if you're within a small niche, this can bring in some really good revenue.
Disadvantages: If one of the major USPs of your blog is your impartiality, then getting a corporate sponsor for your blog could jeopardise this. If you start turning your readers off then it's a downward slope from there.
Another disadvantage of this is that you really need to be fairly established within your niche for companies to want to make the decision of sponsoring you.