Mentorship is vital for early career researchers in training positions, allowing them to navigate the challenges of work and life in research environments. However, the quality of mentorship received by trainees can vary by investigator and by institution. One challenge faced by those hoping to improve trainee mentorship is that the extent to which mentorship is offered to and experienced by research trainees is not well characterized. To address this knowledge gap, we conducted a survey to examine the quality of mentorship received by trainees in research environments, to identify characteristics of positive and negative mentorship, and to highlight best practices to improve trainee mentorship. We received 2,114 responses from researchers at graduate and postdoctoral career stages worldwide. Quantitative analysis showed that at least ~25-45% of respondents were dissatisfied with some aspects of their mentorship. Qualitative responses revealed that common issues in mentorship include unclear expectations in research and mentoring interactions, lack of guidance, and inadequate support of trainee independence and career goals. Our findings also identified key mentorship elements desired by trainee mentees. Based on trainee suggestions, we describe strategies for individual mentors, departments, and institutions to improve the training experience for graduate and postdoctoral researchers.