Literature suggests that students need to be exposed to cognitively demanding tasks (CDT). In this qualitative study, we examined in-service secondary school teachers' challenges in understanding (e.g. recognizing, solving, and designing) and implementing cognitively demanding tasks in mathematics classrooms. Purposive sampling consisted of eleven teachers who completed the cognitive demand survey. Qualitative data sources included semi-structured interviews and classroom observations. Data analysis consisted of open and focused coding based on which the following main challenges were reported: challenges related to students' knowledge, challenges related to English language learners (ELL), challenges related to teachers' knowledge, and challenges related to curriculum. The study results suggest that teachers may need a support system built to address the challenges and to assist in implementing CDT in their classrooms.