Basically, a resume, whatever its format, is a selling document. It showcases your strengths and credentials in the best light for your future employers, post-doctoral fellowship or grant authorities, or anybody who will make the decision on the direction your professional life will take next.
Resumes may be organized in various ways according to the purpose you want them to serve and according to the strengths you would like to highlight. With the resume format for a PhD candidate, you may want to use: a skill-based organization if you don’t have an employment history that does justice to your capabilities; a targeted or customized resume when you apply for a specific job and are well aware of its requirements in terms of skill-sets and competencies; or a (reverse) chronological organization when you have a strong, unbroken record in academia or employment and would like to highlight that history.