Key challenges in cross-cultural counseling include differences in communication styles, cultural values, and beliefs. These challenges can be overcome by developing cultural competence through training and education, actively seeking to understand the client's culture, being open-minded and non-judgmental, and adapting counseling techniques to fit the client's cultural background. Building trust and rapport with the client, acknowledging and addressing any biases or stereotypes, and being willing to learn from the client's perspective are also important in overcoming challenges in cross-cultural counseling.