Short answer — you can usually book Oneworld partner award flights online through several member programs’ websites (but each program has gaps). The best self-service places to try are:

• British Airways Executive Club (ba.com) — BA’s site shows and lets you book most Oneworld partner awards (it’s one of the most comprehensive online partner award engines). (britishairways.com)

• Qantas Frequent Flyer (qantas.com) — Qantas displays award availability for most Oneworld partners and lets you book many partner awards online (with a few specific exceptions). (qantas.com)

• American AAdvantage (aa.com / AA app) — AA’s site includes many Oneworld partners in award search results and lets you book many partner awards online, though not every partner or itinerary appears. (aa.com)

• Alaska Mileage Plan (alaskaair.com) — Alaska’s site lets you search and book lots of partner awards online, but certain partners or routings historically required calling (Cathay/LATAM have had limits). (nerdwallet.com)

• Cathay Pacific Asia Miles (asiamiles.com) and JAL Mileage Bank (jal.co.jp) — both programmes allow online redemptions for many (but not all) partner carriers; each has platform-specific quirks. (upgradedpoints.com)

A couple of important caveats

• No single program displays every Oneworld partner seat. Some programs (notably Qatar Privilege Club in the past) require a phone call or a partner‑award request form for many partner redemptions — even if you can see space elsewhere. If a partner isn’t shown as bookable, you’ll often have to call. (thepointsguy.com)
• Using BA or Qantas as search engines is a common tactic because they show a lot of partner inventory; if one program can’t ticket the flight online you found, try booking with another program that does. (thepointsguy.com)

Practical tips

• Start with BA and Qantas to find availability, then try booking on the program whose miles you actually have (or transfer where allowed). (thepointsguy.com)
• If an online booking fails, the partner may still have space but be blocked on that site — call only as a last resort, or try a different partner program’s website. (news.alaskaair.com)
• Consider award‑search tools (ExpertFlyer, seats.aero, Roame, etc.) to locate space quickly — they help you find availability before you try to book on a program site (many are paid services).

If you want, tell me which airline miles you have and your routing and I’ll tell you the best website(s) to try first and which programs commonly book that route online.