Khovanov homology provides a powerful tool for studying knots and links in 3-space and surfaces in 4-space. I will discuss recent developments that use Khovanov homology to distinguish non-isotopic surfaces in the 4-ball. We will see how braids relate two seemingly disparate strengths of these tools from Khovanov homology: their amenability to calculation (including recent software), and their sensitivity to complex curves. Based on joint work with Isaac Sundberg and with Alan Du.