Definition of dipped tantalum capacitors:
Dipped Tantalum Capacitors, also named radial tantalum capacitors.
they are through-hole components that have leads that extend from the bottom of the capacitor and are bent to fit into holes on the PCB. 
Comparing to SMD tantalum capacitors, they have larger size, cylindrical shape with a metal case that provides protection against mechanical damage and electrical interference.
Widely used in power supplies, audio circuits, TV sets, telecommunications, etc application.

What we should pay attention when using dipped tantalum capacitors?

Below few things should draw our attention:
1)Polarity: they are polarized components, have a positive and negative lead. 
Make sure to connect them to the circuit with the correct polarity, as reversing the polarity can damage the capacitor.

2)Voltage rating: they have a maximum voltage rating, which should not be exceeded. 
Make sure to choose a capacitor with a voltage rating that is appropriate for your circuit.
Pls refer to this file: https://www.hongdacap.com.hk/pdf/Technical_Summary_and_Application_Guidelines_for_Tantalum_Capacitors.pdf

3)Temperature: they are sensitive to high temperatures, which can cause them to fail. 

4)Ripple current: they are often used in circuits that have a high ripple current. 

5)Storage: Tantalum capacitors can degrade over time if they are stored improperly. 
Make sure to store them in a cool, dry place and use them within their recommended shelf life.

Who are the leading players of tantalum capacitors?
Here list top 5 tantalum capacitors manufacturers in the global Tantalum Capacitors market.
Kemet
Kyocera(AVX)
Vishay
Panasonic
Hongda Capacitors https://www.hongdacap.com.hk/

KEMET is the largest manufacture of tantalum capacitor in the world, it has a market share of 35.43% in value. KEMET Corporation, a subsidiary of Yageo Corporation (TAIEX: 2327), manufactures a broad selection of capacitor technologies such as tantalum, aluminum, multilayer ceramic, film, paper, polymer electrolytic, and supercapacitors. KEMET also manufactures a variety of other passive electronic components, such as AC line filters, EMI cores and filters, flex suppressors, electro-mechanical devices (relays), metal composite inductors, ferrite products, and transformers/magnetics. 

AVX is the second largest manufacture of Tantalum capacitor in the world, it has a market share of 15.24% in value. AVX Corporation, is an American manufacturer of electronic components headquartered in Fountain Inn, South Carolina. It is the largest industrial employer in Horry County, South Carolina, with almost 1000 workers in Myrtle Beach and Conway. AVX has 9,900 employees and operates in the United States, Europe and Asia. AVX is a subsidiary of Kyocera Electronics Corporation. AVX has three business units. Passive Components includes electrical components for automotive braking, cell phones, copiers, hearing aids, and locomotives. KED Resale sells Kyocera products including ceramic and tantalum capacitors. Connectors are used in the automotive and medical industries.

Panasonic is the third largest manufacture of Tantalum capacitor in the world, it has a market share of 10.92% in value. Panasonic Corporation, formerly known as the Matsushita Electric Industrial Co., Ltd., founded by Konosuke Matsushita in 1918 as a lightbulb socket manufacturer, is a major Japanese multinational electronics company, headquartered in Kadoma, Osaka. In addition to consumer electronics of which it was the world's largest maker in the late 20th century, Panasonic offers a wide range of products and services, including rechargeable batteries, automotive and avionics systems, industrial systems, as well as home renovation and construction.

Vishay is the fourth largest manufacture of Tantalum capacitor in the world, it has a market share of 9.45% in value. Vishay Intertechnology, Inc. is an American manufacturer of discrete semiconductors and passive electronic components founded by Polish-born businessman Felix Zandman in 1962. Vishay has manufacturing plants in Israel, Asia, Europe, and the Americas where it produces rectifiers, diodes, MOSFETs, optoelectronics, selected integrated circuits, resistors, capacitors, and inductors.

Hongda Capacitors is the largest manufacturer of tantalum capacitors in China, it has a market share of 9% in value. It enjoys very high reputation in China. Hongda Capacitors produce wide range of tantalum capacitors, SOLID TANTALUM MnO2 CAPACITORS, polymer tantalum capacitors, wet tantalum capacitors, high temperature tantalum capacitors, and Oxide Niobium tantalum capacitors in China, which widely used on medical, instruments, military area.

What makes HONGDA Capacitors’ outstanding?
Many brands discontinued dipped tantalum capacitors. But HONGDA Capacitors still produce.
With much stable supply and prices.
Operation temperature up to 125℃
Capacitance up to 1000uF
Replace: AVX TAP, KEMET T350-T390, Nemco TB, Vishay 199D
Can support you samples for test once price, datasheet is accepted.

Below is some high runners: