Start of Summer (pinyin lìxià), which is unconnected to summer solstice, began on May 6th.
立夏
The first character is a pictogram of a person standing up, and carries the general meaning of getting up, hence "getting up to do something", begin.
Grain Full (pinyin xiǎomǎn) started on May 21st.
小满
Although "grain full" is the usual translation, the literal meaning is more like "small full", which is a bit puzzling. Grain is not mentioned at all.