Even though reinforcement-learning-based algorithms achieved superhuman performance in many domains, the field of robotics poses significant challenges as the state and action spaces are continuous, and the reward function is predominantly sparse. Furthermore, on many occasions, the agent is devoid of access to any form of demonstration. Inspired by human learning, in this work, we propose a method named highlight experience replay (HiER) that creates a secondary highlight replay buffer for the most relevant experiences. For the weights update, the transitions are sampled from both the standard and the highlight experience replay buffer. It can be applied with or without the techniques of hindsight experience replay (HER) and prioritized experience replay (PER). Our method significantly improves the performance of the state-of-the-art, validated on 8 tasks of three robotic benchmarks. Furthermore, to exploit the full potential of HiER, we propose HiER+ in which HiER is enhanced with an arbitrary data collection curriculum learning method. Our implementation, the qualitative results, and a video presentation are available on the project site: http://www.danielhorvath.eu/hier/.