Center Controller reported a wake vortex issue with an aircraft behind an A321.

Narrative

I was working Sector X. ZLA [Sector] XY handed me off Aircraft Y; at FL290; requesting FL330 as a final. Aircraft X was handed off about 7 miles behind at FL310. Aircraft Y was slightly slower (about 5 knots; give or take). After updating Aircraft Y on the rides at FL330 (intermittent light chop); I climbed them to FL330 to ensure I had enough time to get them above with the slight overtake. They passed FL310 just west of ZZZ1 (about 5 miles or so). At that time; Aircraft X reported moderate turbulence; bordering on severe. I told the pilot that was my first report of anything more than light chop; then told the supervisor; and; after asking the supervisor if it was needed; asked the pilot if they any injuries or structural problems. The other pilot on Aircraft X then said that it wasn't really severe; but definitely moderate. Aircraft Y then suggested that it was probably them since they two were about 7 miles apart and Aircraft X probably got into the wake of the A321 as they were climbing. The Aircraft X pilot said that was most likely.Earlier in the day; I was on [Sector] YX; having just given a relief briefing. I moved to the D side to help with a flight plan on a no notice F16 split up. There were two A321s climbing off ZZZ2; about 7 miles apart. The back one started complaining about the wake and deviated off course to the right without a clearance. They didn't get within 3 miles of military airspace; but it was pretty close. Sorry; I don't remember the call signs.In the enroute environment; heavy aircraft are not the only ones generating large amounts of wake turbulence. B738s and 9s do as well; and A321s. This is especially problematic with regional aircraft (E75L/CRJs etc) and biz jets. In these two cases; the two aircraft were comparable types; but the front aircraft was generating enough wake turbulence to cause problems with the trailing aircraft. RECAT has been implemented in the terminal environment at many airports; but there has been nothing done in enroute; with the exception of a briefing on the A380; which has been mostly negated by the fact that it isn't flown that much anymore. I think we need more briefings on wake events; information given to controllers on wake turbulence characteristics as they differ between different aircraft; an implantation of RECAT in enroute (with the understanding that 5 miles is not always adequate); a requirement implemented to call traffic based on the actual type instead of a generic 'Airbus' designator as well as traffic information exchanged whenever following problematic types within 10 miles; and the development of a tool to detect wake turbulence conditions that could be worse in certain situations (such as little wind where the wake does not dissipate).In addition; I think a work group should be convened to address these issues; with; at a minimum; the NATCA A114 wake rep.I give permission to allow for the full uncensored version of this report; in its entirety; to all parties.